Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
[deA1] A.D. De Acosta, On the concentration and extension of cylinder measures, Trans. Amer. Math. Soc. 160 (1971) 217–228.
[deA2] A.D. De Acosta, On regular extensions of cylinder measures, Adv. Math. 10 (1973) 329–331.
[Ad1] W. Adamski, τ-smooth Borel measures on topological spaces, Math. Nachr. 78 (1977) 97–107.
[Ad2] W. Adamski, Complete spaces and zero-one measures, Manus. Math. 18 (1976) 343–352.
[Ad3] W. Adamski, Capacity-like functions and upper envelopes of measures, Math. Ann. 229 (1977) 237–244.
[Ad4] W. Adamski, Note on support-concentrated Borel measures, J. Austral. Math. Soc. (Series A) 29 (1980) 310–315.
[Ad5] W. Adamski, On the relations between continuous and nonatomic measures, Math. Nachr. 99 (1980) 55–60.
[Ad6] W. Adamski, An abstract approach to weak topologies in spaces of measures, Bull. Soc. Math. Grèce (N. S.) 18 (1977) 28–68.
[AdGäKa] W. Adamski, P. Gänssler and S. Kaiser, On compactness and convergence in spaces of measures, Math. Ann. 220 (1976) 193–210.
[Al] A.D. Aleksandrov, Additive set-functions in abstract spaces, Mat. Sb. (N.S.) 13 (55) (1943) 169–238.
[AmOkOk] I. Amemiya, S. Okada and Y. Okazaki, Pre-Radon measures on topological spaces, Kodai Math. J. 1 (1978) 101–132.
[An] B. Anger, Representation of capacities, Math. Ann. 299 (1977) 245–258.
[ArPr1] T.E. Armstrong and K. Prikry, Residual measures, Illinois J. Math. 22 (1978) 64–78.
[ArPr2] T.E. Armstrong and K. Prikry, κ-finiteness and κ-additivity of measures on sets and left invariant measures on discrete groups, Proc. Amer. Math. Soc. 80 (1980) 105–112.
[Ba1] A.G.A.G. Babiker, Uniform continuity of measures on completely regular spaces, J. London Math. Soc. (2) 5 (1972) 451–458.
[Ba2] A.G.A.G. Babiker, Uniform regularity of measures on compact spaces, J. Reine Angew. Math., 289 (1977) 188–198.
[Ba3] A.G.A.G. Babiker, On almost discrete spaces, Mathematika 18 (1971) 163–167.
[Ba4] A.G.A.G. Babiker, On uniformly regular topological measure spaces, Duke Math. J. 43 (1976) 775–789.
[Ba5] A.G.A.G. Babiker, Lebesgue measures on topological spaces, Mathematika 24 (1977) 52–59.
[Ba6] A.G.A.G. Babiker, Structural properties of uniformly regular measures on compact spaces, Ann. Soc. Sci. Bruxelles Sér I 90 (1976) 289–296.
[Ba7] A.G.A.G. Babiker, Uniform regularity of measures on locally compact spaces, J. Reine Angew. Math. 298 (1978) 65–73.
[Ba8] A.G.A.G. Babiker, Measurability of sections for maps representing certain measures, J. Reine Angew. Math. 315 (1980) 115–120.
[Ba9] A.G.A.G. Babiker, Uniform regularity of measures on completely regular spaces, to appear.
[Ba10] A.G.A.G. Babiker, Uniformly regular sets of measures on completely regular spaces, preprint.
[Ba11] A.G.A.G. Babiker, Lifting properties and uniform regularity of Lebesgue measures on topological spaces, Mathematika, to appear.
[BaGr] A.G.A.G. Babiker and S. Graf, On H-compact spaces, preprint.
[BaKn1] A.G.A.G. Babiker, and J.D. Knowles, An example concerning regular measures, images of measurable sets and measurable selections, Mathematika 25 (1978) 120–124.
[BaKn2] A.G.A.G. Babiker and J.D. Knowles, Functions and measures on product spaces, preprint.
[BaSa] A.G.A.G. Babiker and A. Sapounakis, Some regularity conditions on topological measure spaces, J. London Math. Soc. (2), 23 (1981) 496–502.
[BaSt ] A.G.A.G. Babiker and W. Strauss, Almost strong liftings and τ-additivity, Proc. Conf. Measure Theory, Oberwolfach 1979, Lecture Notes in Mathematics 794, 220–225.
[BaCo] G. Bachman and R. Cohen, Regular lattice measures and repleteness, Comm. Pure Appl. Math. 26 (1973) 587–599.
[BaSu1] G. Bachman and A. Sultan, Extensions of regular lattice measures with topological applications, J. Math. Anal. App. 57 (1977) 539–559.
[BaSu2] G. Bachman and A. Sultan, Regular lattice measures: mappings and spaces, Pacific J. Math., 67 (1976) 291–321.
[BaSu3] G. Bachman and A. Sultan, On regular extensions of measures, Pacific J. Math. 86 (1980) 389–395.
[BaSu4] G. Bachman and A. Sultan, Measure theoretic techniques in topology and mappings of replete and measure replete spaces, Bull. Austral. Math. Soc. 18 (1978) 267–285.
[BaSu5] G. Bachman and A. Sultan, Representations of linear functionals on spaces of continuous functions, repletions, and general measure extensions, J. Math. Anal. Appl. 67 (1979) 277–293.
[Bad] A. Badrikian, Séminaire sur les fonctions aléatoires linéaires et les mesures cylindriques, Lecture Notes in mathematics 139, Springer-Verlag, Heidelberg, 1970.
[Bel1] A. Bellow, Mesures de Radon et espaces relèvement compacts C.R. Acad. Sci. Paris, Série A, 289 (1979) 621–624.
[Bel2] A. Bellow, Lifting compact spaces, Proc. Conf. Measure Theory, Oberwolfach, 1979, Lecture Notes in Mathematics 794, 233–253.
[Be1] S.K. Berberian, Measure and integration, Macmillan, New York, 1965.
[Be2] S.K. Berberian, On the extension of Borel measures, Proc. Amer. Math. Soc. 16 (1965) 415–418.
[Be3] S.K. Berberian, Sesquiregular measures, Amer. Math. Monthly, 74 (1967) 986–990.
[Be4] S.K. Berberian, Counterexamples in Haar measure, Amer. Math. Monthly, 73 (Part II) (1966) 135–140.
[Bes] A.S. Besicovitch, A general form of the covering principles and relative differentiation of additive functions I, Proc. Camb. Math. Soc. 41 (1945) 103–110; II ibid. Proc. Camb. Math. Soc. 42 (1946) 1–10, corrected, ibid. Proc. Camb. Math. Soc. 43 (1947) 590.
[Bi] K. Bichteler, On the strong lifting property, Illinois J. Math. 16 (1972) 370–380.
[Bla] R. Blair, Closed-completeness in spaces with weak covering properties, in Set-Theoretic Topology, ed. G.M. Reed, Academic Press, New York (1977), p. 17–45.
[Bl] J.H. Blau, The space of measures on a given set, Fund. Math. 38 (1951) 23–34.
[BlMo1] W.W. Bledsoe and A.P. Morse, Product measures, Trans. Amer. Math. Soc. 79 (1955) 173–215.
[BlMo2] W.W. Bledsoe and A.P. Morse, A topological measure construction, Pacific J. Math. 13 (1963) 1067–1084.
[BlWi] W.W. Bledsoe and C.E. Wilks, On Borel product measures, Pacific J. Math. 42 (1972) 569–579.
[Bo] C. Borell, Gaussian Radon measures on locally convex spaces, Math. Scand. 38 (1976) 265–284.
[Br] M. Bruneau, Mesures positives sur la droite réelle; une généralisation du théorème de décomposition de Lebesgue, C.R. Acad. Sci. Paris, Série A, 274 (1972) 1102–1105.
[BrCiGrRy] J. Brzuchowski, J. Cichón, E. Grzegorek and C. Ryll-Nardzewski, On the existence of nonmeasurable unions, Bull. de l'Acad. Pol. des Sci. 27 (1979) 447–448.
[Bu] R.C. Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958) 95–104.
[Ch1] J.R. Choksi, Inverse limits of measure spaces, Proc. London Math. Soc., (3) 8 (1958) 321–342.
[Ch2] J.R. Choksi, Automorphisms of Baire measures on generalized cubes. II, Z. Wahr. verw. Geb. 23 (1972) 97–102.
[Ch3] J.R. Choksi, On compact contents, J. London Math. Soc. 33 (1958) 387–398.
[Ch4] J.R. Choksi, Measurable transformations on compact groups, Trans. Amer. Math. Soc. 184 (1973) 101–124 (1974).
[ChFr] J.R. Choksi and D.H. Fremlin, Completion regular measures on product spaces, Math. Ann. 241 (1979) 113–128.
[Cho] G. Choquet, Lectures on Analysis, Vol. 1, W.A. Benjamin, Inc. New York, 1969.
[Chr] J.P.R. Christensen, The small ball theorem for Hilbert spaces, Math. Ann. 237 (1978) 273–276.
[Cor1] H.H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961) 1–15.
[Cor2] H.H. Corson, Normality in subsets of product spaces, Amer. J. Math. 81 (1959) 785–796.
[Co] G.V. Cox, On Prohorov spaces, preprint.
[Da1] R.O. Davies, Non-σ-finite closed subsets of analytic sets, Proc. Camb. Phil. Soc. 52 (1956) 174–177.
[Da2] R.O. Davies, Increasing sequences of sets and Hausdorff measure, Proc. London Math. Soc. (3) 20 (1970) 222–236.
[Da3] R.O. Davies, Measures of Hausdorff type, J. London Math. Soc. (2) 1 (1969) 30–34.
[Da4] R.O. Davies, Measures not approximable or not specifiable by means of balls, Mathematika 18 (1971) 157–160.
[DaRo] R.O. Davies and C.A. Rogers, The problem of subsets of finite positive measure, Bull. London Math. Soc. 1 (1969) 47–54.
[Dar] R.B. Darst, Two singular measures can agree on balls, Mathematika 20 (1973) 224–225.
[Di] J. Dixmier, Sur certains espaces considérés par M.H. Stone, Summa Brasil. Math. 2 (1951) 151–181. *** DIRECT SUPPORT *** A00J4419 00004
[Duc] M. Duchoň, Sesquiregular measures in product spaces and convolution of such measures, Mat. Časopis Sloven. Akad. Vied. 24 (1974) 31–42.
[Du] R. M. Dudley, Convergence of Baire measures, Studia Math. 27 (1966) 251–268. Correction, Studia Math. 51 (1974) 275.
[Dy] N. Dykes, Generalizations of realcompact spaces, Pacific J. Math. 33 (1970) 571–581.
[Ed1] G. A. Edgar, Measurability in a Banach space, Indiana Univ. Math. J. 26 (1977), 663–677.
[Ed2] G. A. Edgar, Measurability in a Banach space II, Indiana Univ. Math. J. 28 (1979) 559–579.
[Ed3] G. A. Edgar, Disintegration of measures and the vector-valued Radon-Nikodym theorem, Duke Math. J. 42 (1975) 447–450.
[Ed4] G. A. Edgar, Measurable weak sections, Illinois J. Math. 20 (1976) 630–646.
[Ei] L. Q. Eifler, Convex averaging of Radon probability measures, Glasnik Mat. Ser. III 12 (32) (1977) 21–24.
[El1] E. O. Elliott, Measures on product spaces, Trans. Amer. Math. Soc. 128 (1967) 379–388.
[El2] E. O. Elliott, Measures on countable product spaces, Pacific J. Math. 30 (1969) 639–644.
[El3] E. O. Elliott, An extension theorem for obtaining measures on uncountable product spaces, Proc. Amer. Math. Soc. 19 (1968) 1089–1093.
[El4] E. O. Elliott, Limits and extensions of measures, Math. Ann. 187 (1970) 272–278.
[ErKuMa] P. Erdös, K. Kunen, and R. D. Mauldin, Some additive properties of sets of real numbers, preprint.
[ErMa] P. Erdös and R. D. Mauldin, The nonexistence of certain invariant measures, Proc. Amer. Math Soc., 59 (1976) 321–322.
[Fe] H. Federer, Geometric measure theory, Springer-Verlag, New York (1969).
[FiPa] B. Fishel and D. Papert, A note on hyperdiffuse measures, J. London Math. Soc., 39 (1964) 245–254.
[Fl] J. Flachsmeyer, Normal and category measures on topological spaces, Gen. Top. and Relations, III, Prague (1972) 109–116.
[FlLo] J. Flachsmeyer and S. Lotz, A survey on hyperdiffuse measures, I. Proceedings of Conference Topology and Measure (Zinnowitz, 1974), Part 1, 87–128, Ernst-Moritz-Ardnt Univ., Greifswald, 1978.
[Ef1] D. H. Fremlin, Topological Riesz spaces and measure theory, Cambridge University Press, London, 1974.
[Fr2] D. H. Fremlin, Uncountable powers of can be almost lindelöf, Manus. Math. 22 (1977) 77–85.
[Fr3] D. H. Fremlin, Decomposable measure spaces, Z. Wahr. verw. Geb. 45 (1978) 159–167.
[Fr4] D. H. Fremlin, Measurable functions and almost continuous functions, Manus. Math. 33 (1981) 387–405.
[Fr5] D. H. Fremlin, Products of Radon measures: a counter-example, Canad. Math. Bull. 19 (1976) 285–289.
[Fr6] D. H. Fremlin, Pointwise compact sets of measurable functions, Manus. Math. 15 (1975) 219–242.
[Fr7] D. H. Fremlin, Topological measure spaces: two counter-examples, Math. Proc. Camb. Phil. Soc. 78 (1975) 95–106.
[Fr8] D. H. Fremlin, On the Helly space, preprint.
[Fr9] D. H. Fremlin, Counter-example to a “theorem” of A.G.A.G. Babiker, preprint.
[Fr10] D. H. Fremlin, Notes on a paper by R. Po], preprint.
[Fr11] D. H. Fremlin, Hereditarily c. c. c. spaces under Martin's axiom, preprint.
[Fr12] D. H. Fremlin, On the extension of Baire measures, preprint.
[Fr13] D. H. Fremlin, Quasi-Radon measure spaces, preprint dated 10.8.76.
[Fr14] D. H. Fremlin, Quasi-Radon measure spaces, preprint dated 12.9.80.
[Fr15] D. H. Fremlin, Consequences of Martin's axiom, to appear.
[Fr16] D. H. Fremlin, On measurable selections, preprint.
[FrGaHa] D. H. Fremlin, D. J. H. Garling, and R. G. Haydon, Bounded measures on topological spaces, Proc. London Math. Soc. (3) 25 (1972) 115–136.
[FrTa] D. H. Fremlin and M. Talagrand, On the representation of increasing linear functionals on Riesz spaces by measures, Mathematika 25 (1978) 213–215.
[Fro] Z. Frolik, Representation de Riesz des measures uniformes, C. R. Acad. Sci. Paris, Série A 277 (1973) 163–166.
[Gaa] S. A. Gaal, Linear analysis and representation theory, Springer-Verlag, New York, 1973.
[Gai] S. Gaina, Sur les notions de mesure compacte et de mesure régulière, Ann. Fac. Sci. Univ. Nat. Zäire (Kinshasa) Sect. Math.-Phys 2 (1976) 71–79.
[Gä1] P. Gänssler, A convergence theorem for measures in regular Hausdorff spaces, Math. Scand. 29 (1971) 237–244.
[Gä2] P. Gänssler, Compactness and sequential compactness in spaces of measures. Z. Wahr. verw. Geb. 17 (1971) 124–146.
[Ga1] R. J. Gardner, The regularity of Borel measures and Borel measurecompactness, Proc. London Math. Soc. (3) 30 (1975) 95–113.
[Ga2] R. J. Gardner, Problems in measure theory, Ph.D. Thesis, London University, 1974.
[GaGr] R. J. Gardner and G. Gruenhage, Finite Borel measures on space of cardinality less than c, Proc. Amer. Math. Soc. 81 (1981) 624–628.
[GaPf1] R. J. Gardner and W. F. Pfeffer, Some undecidability results concerning Radon measures, Trans. Amer. Math. Soc. 259 (1980) 65–74.
[GaPf2] R. J. Gardner and W. F. Pfeffer, Are diffused, regular, Radon measures σ-finite? J. London Math. Soc. (2) 20 (1979) 485–494.
[GaPf3] R. J. Gardner and W. F. Pfeffer, Relation between the regularity and σ-finiteness of Radon measures, Uspekhi Matematicheskikh Nauk., (in Russian) 35 [3(213)] (1980) 31–36.
[Ge] P. Gerard, Spaces of measures associated to a family of functions, Bull. Soc. Roy. Sci. Liège, 44 (1975) 501–534.
[Gl] L. Gluck, On characterization of absolutely continuous measures on locally compact spaces, Monat. Math. 77 (1973) 206–210.
[GoSi] M. C. Godfrey and M. Sion, On product of Radón measures, Canad. Math. Bull. 12 (1969) 427–444.
[GoMa] G. G. Gould and M. Mahowald, Measures on completely regular spaces, J. London Math. Soc. 37 (1962) 103–111.
[Go] C. Gowrisankaran, Semigroups with invariant Radon measures, Proc. Amer. Math. Soc. 38 (1973) 400–404.
[Gow] K. Gowrisankaran, Measurability of functions in product spaces, Proc. Amer. Math. Soc. 31 (1972) 485–488.
[Gra] S. Graf, Induced σ-homomorphisms and a parametrization of measurable selections via extremal preimage measures, Math. Ann. 247 (1980) 67–80.
[Gr] E. Granirer, On Baire measures on D-topological spaces, Fund. Math. 60 (1967) 1–22.
[Grö] W. Grömig, On a weakly closed subset of the space of τ-smooth measures, Proc. Amer. Math. Soc. 43 (1974) 397–401.
[Gro] A. Grothendieck, Sur les applications lineares faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953) 129–173.
[GrGa] G. Gruenhage and R. J. Gardner; Completeness and weak covering properties, and measure-compactness, J. London Math. Soc., (2) 18 (1978) 316–324.
[GrPf] G. Gruenhage and W. F. Pfeffer, When inner regularity of Borel measures implies regularity, J. London Math. Soc., (2) 17 (1978) 165–171.
[Gu1] P. J. Guerra, Compactness in the space of Radon measures of type (H) Proc. Roy. Irish Acad. Sect A. 78 (1978) 199–216.
[Gu2] P. J. Guerra, Stability of tensor products of Radon measures of type (H), Proc. Conf. Vector Measures and Applications II, Dublin 1977, Lecture Notes in Mathematics 645, 97–108.
[Gu3] P. J. Guerra, Net convergence of projective limits of Radon measures (Spanish) Collect. Math. 29 (1978) 11–20.
[HaReRi] A. W. Hager, G. D. Reynolds, and M. D. Rice, Borel-complete topological spaces, Fund. Math. 75 (1972) 135–143.
[Hah] P. Hahn, Haar measure for measure groupoids, Trans. Amer. Math. Soc. 242 (1978) 1–33.
[Ha] P. R. Halmos, Measure theory, Van Nostrand, New York, 1950.
[HaLa] J. Hardy and H. E. Lacey, Extension of regular Borel measures, Pacific J. Math. 24 (1968) 277–282.
[HaSi] F. Harpain and M. Sion, A representation theorem for measures on infinite dimensional spaces, Pacific J. Math 30 (1969) 47–58.
[Hay1] R. Haydon, On compactness in spaces of measures and measure-compact spaces, Proc. London Math. Soc. 29 (1974) 1–16.
[Hay2] R. Haydon, On dual L1-spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978) 142–152.
[HeLa] D. J. Hebert and H. Elton Lacey, On supports of regular Borel measures, Pacific J. Math., 27 (1968) 101–117.
[Heb] M. Heble, Probability measures on certain compact semigroups, J. Math. Anal. Appl. 8 (1964) 258–277.
[He] D. Heidemann, On the extension of cylinder measures to τ-smooth measures in linear spaces, Proc. Amer. Math. Soc. 61 (1976) 59–65.
[HeSt ] E. Hewitt and K. Stromberg, Real and abstract analysis, Springer-Verlag, Heidelberg, 1965.
[Hey] H. Heyer, Probability measures on locally compact groups, Springer-Verlag, Berlin, 1977.
[Ho] J. Hoffman-Jørgensen, Weak compactness and tightness of subsets of M(X), Math. Scand. 31 (1972) 127–150. *** DIRECT SUPPORT *** A00J4419 00005
[Hu] R.E. Huff, Sigma-finiteness and Haar measure, Amer. Math. Monthly 76 (1969) 1042–1043.
[IoIo] A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Springer-Verlag, New York, 1969.
[Is] T. Ishii, On semi-reducible measures II, Proc. Japan. Acad. 32 (1956) 241–244.
[Ja] R.E. Jamison, A quick proof for a one-dimensional version of Liapounoff's theorem, Amer. Math. Monthly 81 (1974) 507–508.
[Jo1] R.A. Johnson, On the Lebesque decomposition theorem, Proc. Amer. Math. Soc. 18 (1967) 628–632.
[Jo2] R.A. Johnson, Some types of Borel measures, Proc. Amer. Math. Soc. 22 (1969) 94–99.
[Jo3] R.A. Johnson, Atomic and nonatomic measures, Proc. Amer. Math. Soc. 25 (1970) 650–655.
[Jo4] R.A. Johnson, On product measures and Fubini's theorem in locally compact spaces, Trans. Amer. Math. Soc. 123 (1966) 112–129.
[Jo5] R.A. Johnson, Some relationships between measures, Pacific J. Math. 82 (1979) 117–132.
[Jo6] R.A. Johnson, Measurability of cross section measure of a product Borel set, J. Austral. Math. Soc. (Series A) 28 (1979) 346–352.
[Jo7] R.A. Johnson, Nearly Borel sets and product measures, Pacific J. Math. 87 (1980) 97–109.
[Jo8] R.A. Johnson, Another Borel measure-compact space which is not weakly Borel measure-complete, J. London Math. Soc. (2) 21 (1980), 263–264.
[Jo9] R.A. Johnson, Extending the product of two regular Borel measures, Illinois J. Math. 24 (1980) 639–644.
[Jo10] R.A. Johnson, Products of two Borel measures, preprint.
[Jo11] R.A. Johnson, private communication.
[JoRo] R.A. Johnson and C.A. Rogers, Hausdorff measure and local measure, preprint.
[Joh] B.E. Johnson, Separate continuity and measurability, Proc. Amer. Math. Soc. 20 (1969), 420–422.
[Jos] W. Josephson, Coallocation between lattices with applications to measure extensions, Pacific J. Math. 75 (1978) 149–163.
[Ju] I. Juhász, Cardinal functions in topology, Math. Centre Tracts No. 34, Mathematisch Centrum, Amsterdam, 1971.
[JuKuRu] I. Juhász, K. Kunen and M.E. Rudin, Two more hereditarily separable non-Lindelöf spaces, Canad. J. Math. 5 (1976) 998–1005.
[Ka] S. Kakutani, Notes on infinite product measures, II. Proc. Imperial Acad. Tokyo 19 (1943) 184–188.
[KaKo] S. Kakutani and K. Kodaira, Über des Haarsche Maß in der lokal bikompacten Gruppe, Proc. Imperial Acad. Tokyo 20 (1944) 444–450.
[Kal] G. Kallianpur, The topology of weak convergence of probability measures, J. Math. Mech. 10 (1961) 947–969.
[KaRa] V. Kannan and S.R. Raju, The nonexistence of invariant universal measures on semigroups, Proc. Amer. Math. Soc. 78 (1970) 482–484.
[Kat] M. Katětov, Measures in fully normal spaces, Fund. Math. 38 (1951) 73–84.
[KeNa] J.L. Kelley, and I. Namioka, Linear topological spaces, Springer-Verlag, New York, 1963.
[KeSr] J.L. Kelley and T.P. Srinivasan, Pre-measures on lattices of sets, Math. Ann. 190 (1970/1) 233–241.
[Ke1] J.D. Kelly, A method for constructing measures appropriate to the study of Cartesian products, Proc. London Math. Soc. (3) 26 (1973) 521–546.
[Ke2] J.D. Kelly, The increasing sets lemma for the measures generated by method III, J. London Math. Soc. (2) 8 (1974) 29–43.
[KeMa] J.H.B. Kemperman and D. Maharam, ℝc is not almost Lindelöf, Proc. Amer. Math. Soc. 21 (1970) 772–773.
[Ker] M. Kerner, Lattice measures, realcompactness and pseudocompactness II, Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur. (8) 59 (1975) 603–610 (1976).
[Kh] V.-K. Khoan, Une remarque sur les mesures de Radon et les mesures abstraites, C.R. Acad. Sci. Paris, Serie A, 272 (1971) 1383–1386.
[Ki1] R.B. Kirk, Measures in topological spaces and B-compactness, Nederl. Akad. Wetensch. Proc. Ser. A 72 (1969) 172–183.
[Ki2] R.B. Kirk, Locally compact, B-compact spaces, Nederl. Akad. Wetensch. Proc. Ser. A 72 (1969) 333–344.
[Ki3] R.B. Kirk, Convergence of Baire measures, Pacific J. Math. 49 (1973) 135–148.
[Ki4] R.B. Kirk, Kolmogorov type consistency theorems for products of locally compact, B-compact spaces, Nederl. Akad. Wetensch. Proc. Ser. A 73=Indig. Math. 32 (1970) 77–81.
[Kis] J. Kisyński, On the generation of tight measures, Studia Math. 30 (1968) 141–151.
[Kn1] J.D. Knowles, Measures on topological spaces, Proc. London Math. Soc. (3) 17 (1967) 139–156.
[Kn2] J.D. Knowles, On the existence of non-atomic measures, Mathematika 14 (1967) 62–67.
[Ko1] G. Komoullis, On perfect measures, Trans. Amer. Math. Soc. 264 (1981) 521–537.
[Ko2] G. Koumoullis, On the almost Lindelöf property in products of separable metric spaces, preprint.
[Ko3] G. Koumoullis, Some topological properties of spaces of measures, to appear in Pacific J. Math.
[KoSa] G. Koumoullis and A. Sapounakis, Two countability properties of sets of measures, preprint.
[KuSm] M. Kuczma and J. Smîtal, On measures connected with the Cauchy equation, Aequationes Math. 14 (1976) 421–428.
[Ku1] K. Kunen, A compact L-space, Topology and its App. 12 (1981) 283–287.
[Ku2] K. Kunen, Some points in βN, Math. Proc. Camb. Phil. Soc. 80 (1976) 385–398.
[La1] D.G. Larman, The approximation of Gδ-sets, in measure, by Fσ-sets, Proc. Camb. Phil. Soc. 61 (1965) 105–107.
[La2] D.G. Larman, On the selection of compact subsets of positive measure from analytic subsets of positive measure, Canad. J. Math. 26 (1974) 665–677.
[LeC] L. Le Cam, Convergence in distribution of stochastic processes, Univ. Calif. Publ. Statist. 2 (1957) 207–236.
[Le1] J. Lembcke, Konservative Abbildungen und Fortsetzung regulärer Maße, Z. Wahr. Verw. Geb. 15 (1970) 57–96.
[Le2] J. Lembcke, Reguläre Masse mit einer gegebenen Familie von Bildmassen, Bayer. Akad. Wiss. Math.—Nat. Kl. Sitzungsber. (1976) 61–115 (1977).
[LeSt ] M. Levin and W. Stiles, On the regularity of measures on locally compact spaces, Proc. Amer. Math. Soc., 36 (1972) 201–206.
[LeLe] J. Lewin and M. Lewin, A reformulation of the Radon-Nikodým theorem, Proc. Amer. Math. Soc., 47 (1975) 393–400.
[Lin] D.A. Lind, Convolutions and absolute continuity, Proc. Amer. Math. Soc. 39 (1973) 347–348.
[Lo] V. Losert, A measure space without the strong lifting property, Math. Ann. 239 (1979) 119–128.
[Lu1] N.Y. Luther, Lebesque decomposition and weakly Borel measures, Duke Math. J. 35 (1968) 601–615.
[Lu2] N.Y. Luther, A note on regular and anti-regular (weakly) Borel measures, Duke Math. J. 38 (1971) 147–149.
[Lu3] N.Y. Luther, Completion regularity of (weakly) Borel measures, Duke Math. J. 37 (1970) 11–19.
[Lu4]N.Y. Luther, Weak denseness of nonatomic measures on perfect, locally compact spaces, Pacific J. Math. 34 (1970) 453–460.
[Lu5] N.Y. Luther, Locally compact spaces of measures, Proc. Amer. Math. Soc. 25 (1970) 541–547.
[Ma1] D. Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942) 108–111.
[Ma2] D. Maharam, On smoothing compact measure spaces by multiplication, Trans. Amer. Math. Soc. 204 (1975) 1–39.
[Mal] D.J. Mallory, Topological properties of limits of inverse systems of measures, Canad. J. Math. 26 (1974) 1455–1465.
[Mar] E. Marczewski, On compact measures, Fund. Math. 40 (1953) 113–124.
[MaSi] E. Marczewski and R. Sikorski, Measures in non-separable metric spaces, Colloq. Math. 1 (1948) 133–149.
[Mař] J. Mařik, The Baire and Borel measure, Czech. Math. J. 7 (82) (1957) 248–253.
[Mart] A.F. Martin, A note on monogenic Baire measures, Amer. Math. Monthly 84 (1977) 554–555.
[MaSo] D.A. Martin and R.M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970) 143–178.
[Mau] R.D. Mauldin, The existence of non-measurable sets, Amer. Math. Monthly, 86 (1979) 45–46.
[McK] J.R. McKinney, Kernels of measures on completely regular spaces, Duke Math. J. 40 (1973) 915–923.
[MiRu] E. Michael and M.E. Rudin, A note on Eberlein compacts, Pacific J. Math. 72 (1977) 487–495.
[Mo1] W. Moran, The additivity of measures on completely regular spaces, J. London Math. Soc. 43 (1968) 633–639.
[Mo2] W. Moran, Measures and mappings on topological spaces, Proc. London Math. Soc. (3) 19 (1969) 493–508. *** DIRECT SUPPORT *** A00J4419 00006
[Mo3] W. Moran, Measures on metacompact spaces, Proc. London Math Soc. (3) 20 (1970) 507–524.
[Mo4] W. Moran, Separate continuity and supports of measures, J. London Math. Soc. 44 (1969) 320–324.
[MoWh] S.E. Mosiman and R.F. Wheeler, The strict topology in a completely regular setting: relations to topological measure theory, Canad. J. Math. 24 (1972) 873–890.
[Mu] A. Mukherjea, A remark on Tonelli's theorem on integration in product spaces, Pacific J. Math. 42 (1972) 177–185.
[Mun] M.E. Munroe, Introduction to measure and integration, Addison-Wesley, Reading, Mass. U.S.A., 1953.
[MuS1] K. Musial, Interitness of compactness and perfectness of measures by thick subsets, Lecture Notes in Mathematics 541 (1976) 31–42.
[MuS2] K. Musial, Projective limits of perfect measure spaces, Fund. Math. 110 (1980) 163–189.
[My] J. Mycielski, Remarks on invariant measures in metric spaces, Colloq. Math. 32 (1974) 105–112.
[vN] J. von Neumann, Einige Sätze über meßbare Abbildungen, Ann. of Math. 33 (1932) 574–586.
[OgZu] S. Ogawa and C. Zuppa, Measures on some topological spaces, Math. Japon. 19 (1974) 117–120.
[Oh] H.S. Oh, Notes on atomic measures, Kyungpook Math. J., 10 (1970) 81–83.
[Ok] S. Okada, Supports of Borel measures, J. Austral. Math. Soc. (Series A) 27 (1979) 221–231.
[OkOk1] S. Okada and Y. Okazaki, On measure-compactness and Borell measurecompactness. Osaka J. Math. 15 (1978) 183–191.
[OkOk2] S. Okada and Y. Okazaki, Projective limit of infinite Radon measures, J. Austral. Math. Soc. (Series A) 25 (1978) 328–331.
[Ol] V. Olejček, Darboux property of regular measures, Mat. Časopis Sloven. Akad. Vied. 24 (1974) 283–288.
[Op] V. Oppel, Zur schwachen Topologie auf dem Vektorraum der Borel-Maße polonischer und Lusinscher Räume, Math. Z. 147 (1976) 97–99.
[Os] A.J. Ostaszewski, Absolutely non-measurable and singular co-analytic sets, Mathematika 22 (1975) 161–163.
[Ox1] J.C. Oxtoby, Spaces that admit a category measure, J. Reine. Angew. Math. 205 (1961) 156–170.
[Ox2] J.C. Oxtoby, Measure and category, 2nd Edition, Springer-Verlag, New York, 1980.
[Ox3] J.C. Oxtoby, Homeomorphic measures in metric spaces, Proc. Amer. Math. Soc. 24 (1970) 419–423.
[Pa] J. K. Pachl, Two classes of measures, Colloq. Math. 42 (1979) 331–340.
[PaSe] R. Panzone and C. Segovia, Measurable transformations on compact spaces and o.n. systems on compact groups, Rev. Un. Mat. Argentina 22 (1964) 83–102.
[Pe1] H.L. Peterson, Regular and irregular measures on groups and dyadic spaces, Pacific J. Math. 28 (1969) 173–182.
[Pe2] H.L. Peterson, Irregular invariant measures related to Haar measure, Proc. Amer. Math. Soc. 24 (1970) 356–361.
[Pet] B.J. Pettis, On the extension of measures, Ann. of Math. 54 (1951) 186–197.
[Pfa] J. Pfanzagl, Convergent sequences of regular measures, Manus. Math. 4 (1971) 91–98.
[Pf1] W.F. Pfeffer, Integrals and measures, Marcel Dekker, New York, 1977.
[Pf2] W.F. Pfeffer, On the regularity of Borel measures, Math. Colloq. Univ. Cape Town 8 (1973) 125–142.
[Pf3] W.F. Pfeffer, Some remarks on generalized Borel measures in topological spaces, Proc. 1977 Topology Conf. Louisiana State Univ. Vol. 2, 543–562.
[Pl] D. Plachky, Decomposition of additive set functions, Trans. Sixth Prague Conf. Information Theory, Technical Univ. Prague, Prague. 1971, 715–719. Academia, Prague, 1973.
[Po1] R. Pol, Note on the spaces P(S) of regular probability measures whose topology is determined by countable subsets, preprint.
[Po2] R. Pol, The spaces P(S) of regular probability measures whose topology is determined by countable subsets, in General Topology and Modern Analysis, L.F. McAuley and M.M. Rao, Academic Press, 1980.
[Pol] R. Polexe, Sur la regularité des measures absolument continues et singulières, Bul., Univ. Brasov Ser. C. Mat. Fiz. Chim. Sti. Natur. 15 (1973) 25–28.
[PoTo] D. Pollard and F. Topsøe, A unified approach to Riesz type representation theorems, Studia Math. 54 (1975) 173–190.
[Pre] D. Preiss, Metric spaces in which Prohorov's theorem is not valid, Z. Wahr. verw. Geb. 27 (1973) 109–116.
[PrSo] K. Prikry and R.M. Solovay, Images of measures on separable metric spaces, preprint.
[Pro] Y.V. Prohorov, Convergence of random processes and limit theorems in probability theory, Theor. Prob. Appl. 1 (1956) 157–214.
[RaRa] M.B. Rao and K.P.S.B. Rao, Borel σ-algebra on [0,Ω], Manus. Math. 5 (1971) 195–198.
[Re] P. Ressel, Some continuity and measurability results on spaces of measures, Math. Scand. 40 (1977) 69–78.
[RiRe] M.D. Rice and G.D. Reynolds, Weakly Borel-complete topological spaces, Fund. Math. 105 (1980) 179–185.
[Ri] B. Riečan, Regularity and approximation theorems for measures and integrals, Mat. Časopis Sloven. Akad. Vied. 24 (1974) 209–224.
[Rie1] Z. Riečanová, A note on weakly Borel measures, Časopis Pěst. Mat. 97 (1972) 47–49, 94.
[Rie2] Z. Riečanová, On two strengthenings of regularity of measures, Math. Slovaca 30 (1980) 281–288.
[Rob] J.W. Roberts, Invariant measures in compact Hausdorff spaces, Indiana Univ. Math. J. 24 (1975) 691–718.
[Ro] C.A. Rogers, Hausdorff measures, Cambridge University Press, Cambridge, 1970.
[RoSi] C.A. Rogers and M. Sion, On Hausdorff measures in topological spaces, Monat. Math. 67 (1963) 269–278.
[Ros] H.P. Rosenthal, The hereditary problem for weakly compactly generated Banach spaces, Compositio Math. 28 (1974) 83–111.
[Rud] W. Rudin, Fourier analysis on groups, Interscience, New York, 1962.
[Ry] C. Ryll-Nardzewski, On quasi-compact measures, Fund. Math. 40 (1953) 125–130.
[RyTe] C. Ryll-Nardzewski and R. Telgársky, The nonexistence of universal invariant measures, Proc. Amer. Math. Soc. 69 (1978) 240–242.
[Sa] J. Saint-Pierre, Desintégration d'une mesure non bornée, Ann. Inst. Henri Poincaré, Sect. B (N.S.) 11 (1975) 275–286.
[Sai] J. Saint-Raymond, Caractérisation d'espaces polonais. D'après des travaux recents de J.P.R. Christensen et D. Preiss. Séminaire Choquet, 11e–12e années (1971–1973), Initiation à l'analyse, Commun. No. C1, 2pp., Secrétariat Mathématique, Paris, 1975.
[SaGu1] B.R. Salinas and P.J. Guerra, Radon spaces of type (H) (Spanish) Rev. Real Acad. Ci. Exact. Fis. Natur. Madrid 69 (1975) 761–774.
[SaGu2] B.R. Salinas and P.J. Guerra, Radon measures of type (H) in arbitrary topological spaces (Spanish), Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 10, 190 pp. (1970)
[Sap] A. Sapounakis, Measures on totally ordered spaces, Mathematika 27 (1980) 225–235.
[SaOk] H. Sato and Y. Okazaki, Separabilities of a Gaussian Radon measure, Ann. Inst. Henri Poincaré B, 11 (1975) 287–298.
[Saz] V.V. Sazonov, On perfect measures, Amer. Math. Soc. Transl. (2) 48 (1965) 229–254.
[Sch1] W. Schachermayer, Eberlein-compacts et espaces de Radon, C.R. Acad. Sci. Paris, Série A, 284 (1977) 405–407.
[Sch2] W. Schachermayer, Mesures cylindriques sur les espaces de Banach, qui ont la propriété de Radon-Nikodym, C.R. Acad. Sci. Paris, Série A 282 (1976) 227–229.
[Sch3] W. Schachermayer, On compact spaces which are not c-spaces, Bol. de la Soc. Mat. Mexicana 22 (1977) 60–63.
[Sc1] L. Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Oxford Univ. Press, London, 1973.
[Sc2] L. Schwartz, Certaines propriétés des measures sur les espaces de Banach, Seminaire Maurey-Schwartz (1975–1976), Espaces LP, applications radonificantes et géometrié des espaces de Banach, Exp. No. 23, Centre Math., École Polytech., Palaiseau, 1976.
[Seg] I.E. Segal, Equivalences of measure spaces, Amer. J. Math 73 (1951) 275–313.
[Sem] Z. Semadeni, Banach spaces of continuous functions, Volume 1, Polish Scientific Publishers, Warsaw, 1971.
[Se1] F.D. Sentilles, Existence of regular finite invariant measures for Markov processes, Proc. Amer. Math. Soc. 21 (1969) 318–320.
[Se2] F.D. Sentilles, Bounded continuous functions on a completely regular space, Trans. Amer. Math. Soc., 168 (1972) 311–336.
[SeWh] D. Sentilles and R.F. Wheeler, Linear functionals and partitions of unity in Cb(X), Duke Math. J. 41 (1974) 483–496.
[Sh] S. Shelah, You cannot take Solovay's inaccessible, away, Abstracts Amer. Math. Soc. 1 (1980) 236.
[Si] E. Siebert, Convergence and, convolutions of probability measures on a topological group, Ann. Prob. 4 (1976) 433–443. *** DIRECT SUPPORT *** A00J4419 00007
[SiSj] M. Sion and D. Sjerve, Approximation properties of measures generated by continuous set functions. Mathematika 9 (1962) 145–146.
[SiWi] M. Sion and R.C. Willmott, Hausdorff measures on abstract spaces, Trans. Amer. Math. Soc. 123 (1966) 275–309.
[Sm] W.L. Smith, A generalized infinite product measure, Duke Math. J. 38 (1971) 765–769.
[So] R. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970) 1–56.
[SpJe] E. Sparre Andersen and B. Jessen, On the introduction of measures in infinite product sets, Danske Vid. Selsk. Math.-Fys. Medd. 25 (1948) No. 4.
[StSe] L. Steen and J. Seebach, Counterexamples in topology, Holt, Rinehart and Winston, New York, 1970.
[Ste1] J.D. Stein, Jr. Uniform absolute continuity in spaces of set functions, Proc. Amer. Math. Soc. 51 (1975) 137–140.
[Ste2] J.D. Stein, Jr., A uniform-boundedness theorem for measures, Michigan Math. J. 19 (1972) 161–165.
[Stei] R.C. Steinlage, On Haar measure in locally compact T2 spaces, Amer. J. Math. 97 (1975) 291–307.
[Št ] J. Štěpán, On the family of translations of a tight probability measure on a topological group, Z. Wahr. verw. Geb. 15 (1970) 131–138.
[Str] P.D. Stratigos, A general measure decomposition theorem, by means of the general Wallman remainder, Proc. Conf. Measure Theory and Its Applications, Northern Illinois Univ. DeKalb, Illinois (1980) 261–267.
[Sul1] A. Sultan, A general measure extension procedure, Proc. Amer. Math. Soc. 69 (1978) 37–45.
[Sul2] A. Sultan, Measure, compactification and representation, Canad. J. Math. 30 (1978) 54–65.
[Su] C. Sunyach, Une caractérisation des espaces universellement Radonmesurables, C.R. Acad. Sci. Paris, Série A, 268 (1969) 864–866.
[Sw] G. Swift, Irregular Borel measures on topological spaces, Duke Math. J. 22 (1955) 427–433.
[Sz] M. Szeto, Measure repleteness and mapping preservations, J. Indian Math. Soc., to appear.
[Ta1] M. Talagrand, Espaces de Banach faiblement K-analytiques, C.R. Acad. Sci. Paris, Série A, 284 (1977) 745–748.
[Ta2] M. Talagrand, Sur une conjecture de H. H. Corson, Bull. Sc. Math. (2) 99 (1975) 211–212.
[Ta3] M. Talagrand, Sur les espaces de Banach faiblement K-analytique, C. R. Acad. Sci. Paris, Série A, 285 (1977) 119–122.
[Ta4] M. Talagrand, Sur un théorème de L. Schwartz, C.R. Acad. Sci. Paris, Série A, 286 (1978) 265–267.
[Ta5] M. Talagrand, Les mesures gaussiennes qui ne sont pas de Radon, C.R. Acad. Sci. Paris, Série A, 291 (1980) 223–225.
[Ta6] M. Talagrand, La τ-regularité des mesures gaussiennes, Z. Wahr. verw. Geb. 57 (1981) 213–221.
[Ta7] M. Talagrand, Mesures gaussiennes sur un espace localement convexe, Z. Wahr. verw. Geb., to appear.
[Ta8] M. Talagrand, Espaces de Banach faiblement K-analytiques, Annals of Math., to appear.
[To1] F. Topsøe, Topology and measure, Lecture Notes in Math. 133, Springer-Verlag (1970).
[To2] F. Topsøe, Compactness and tightness in a space of measures with the topology of weak convergence, Math. Scand. 34 (1974) 187–210.
[To3] F. Topsøe, Some special results on convergent sequences of Radon measures, Manus. Math. 19 (1976) 1–14.
[To4] F. Topsøe, Approximating pavings and construction of measures, Colloq. Math. 42 (1979) 377–385.
[To5] F. Topsøe, On construction of measures, Proceedings of Conference Topology and Measure (Zinnowitz, 1974), Part 1, 343–381, Ernst-Moritz-Arndt. Univ., Greifswald, 1978.
[Tor1] A. Tortrat, τ-régularité des lois, séparation au sens de A. Tulcea et propriété de Radon-Nikodym, Ann. Inst. Henri Poincaré B, 12 (1976) 131–150. Addendum, Ann. Inst. Henri Poincaré B, 13 (1977) 43.
[Tor2] A. Tortrat, Prolongements τ-réguliers; Application aux probabilités gaussiennes. Symposia Mathematica Vol. XXI, (1977) 117–138.
[TsKa1] N.A. Tserpes and A.G. Kartsatos, On semi-invariant probability measures on semigroups, Z. Wahr. verw. Geb. 15 (1970) 260–262.
[TsKa2] N.A. Tserpes and A.G. Kartsatos, Mesures semi-invariantes sur un semigroupe localement compact, C.R. Acad. Sci. Paris, Série A, 267 (1968) 507–509.
[Ts] B. Tsirel'son, Natural modification of stochastic processes and its applications to series of stochastic functionals and Gaussian measures, Zapiski Nautchni Seminarov LOM 55(1976).
[Ul] S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930) 140–150.
[Val] M. Valadier, Désintégration d'une mesure sur un produit, C.R. Acad. Sci. Paris, Série A, 276 (1973) 33–35.
[Va] V.S. Varadarajan, Measures on topological spaces, Amer. Math. Soc. Transl. (2) 48 (1965) 161–228.
[Wa1] M.L. Wage, The product of Radon spaces (Russian), International Topology Conference (Moscow State Univ., Moscow, 1979) Uspehi Mat. Nauk 35 (1980) No. 3 (213) 151–153.
[Wa2] M.L. Wage, A generalization of Lusin's theorem, Proc. Amer. Math. Soc. 52 (1975) 327–332.
[WeDeV] R.C. Welland and A. De Vito, A characterization of absolute continuity, J. Math. Anal. Appl. 20 (1967) 256–261.
[We] B.B. Wells, Jr., Weak compactness of measures, Proc. Amer. Math. Soc. 20 (1969) 124–134.
[Wh1] R.F. Wheeler, The strict topology, separable measures, and paracompactness, Pacific J. Math. 47 (1973) 287–302.
[Wh2] R.F. Wheeler, The strict topology for P-spaces, Proc. Amer. Math. Soc., 41 (1973) 466–472.
[Wh3] R.F. Wheeler, On separable z-filters, Gen. Top. Appl. 5 (1975) 333–345.
[Wh4] R.F. Wheeler, Article to appear in Expositiones Mathematicae.
[Wh5] R.F. Wheeler, Extensions of a σ-additive measure to the projective cover, Proc. Conf. Measure Theory, Oberwolfach 1979, Lecture Notes in Mathematics 794, 81–104.
[Wi] W.J. Wilbur, On measurability and regularity, Proc. Amer. Math. Soc. 21 (1969) 741–746.
[WoLe] J. Woo and J. Lee, A note on atomic measure and singularity, Kyungpook Math, J. 10 (1970) 85–88.
[Ya] N. N. Yakolev, On bicompacta in Σ-products and related spaces, Comm. Math. Univ. Carol. 21 (1980) 263–282.
[Zaa] A.C. Zaanen, The Radon-Nikodym theorem, I and II, Indig. Math. 23 (1961) 157–187.
[Za] E. Zakon, A note on regular measures, Canad. Math. Bull. 7 (1964) 41–44.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Gardner, R.J. (1982). The regularity of borel measures. In: Kölzow, D., Maharam-Stone, D. (eds) Measure Theory Oberwolfach 1981. Lecture Notes in Mathematics, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096664
Download citation
DOI: https://doi.org/10.1007/BFb0096664
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11580-9
Online ISBN: 978-3-540-39324-5
eBook Packages: Springer Book Archive