Skip to main content

Vector Measures and Dominated Mappings

  • Chapter
Nonstandard Analysis and Vector Lattices

Part of the book series: Mathematics and Its Applications ((MAIA,volume 525))

  • 378 Accesses

Abstract

The modern vector measure theory contains two weakly interacting directions of research.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dinculeanu N., Vector Measures, VEB Deutscher Verlag der Wissenschaften, Berlin (1966).

    MATH  Google Scholar 

  2. Diestel J. and Uhl J. J., Vector Measures, Amer. Math. Soc., Providence, RI (1977). (Math. Surveys; 15.)

    Google Scholar 

  3. Kantorovich L. V., Vulikh B. Z., and Pinsker A. G., Functional Analysis in Semiordered Spaces [in Russian], Gostekhizdat, Moscow and Leningrad (1950)

    Google Scholar 

  4. Fremlin D. M., “A direct proof of the Matthes—Wright integral extension theorem,” J. London Math. Soc. (2), 11, No. 3, 276–284 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  5. Riečan B., “A simplified proof of the Daniell integral extension theorem in ordered spaces,” Math. Slovaca, 32, No. 1, 75–79 (1982).

    MathSciNet  MATH  Google Scholar 

  6. Hausdorff F., Set Theory, Chelsea, New York (1991).

    MATH  Google Scholar 

  7. Plesner A. I., Spectral Theory of Linear Operators. Vol. 1 and 2, Frederick Ungar Publishing Co., New York (1969).

    MATH  Google Scholar 

  8. Vulikh B. Z., Introduction to Functional Analysis, Pergamon Press, Oxford (1963).

    MATH  Google Scholar 

  9. Kusraev A. G., Vector Duality and Its Applications [in Russian], Nauka, Novosibirsk (1985).

    Google Scholar 

  10. Kusraev A. G. and Strizhevskiĭ V. Z., “Lattice normed spaces and dominated operators,” in: Studies on Geometry and Functional Analysis. Vol. 7 [in Russian], Trudy Inst. Mat. (Novosibirsk), Novosibirsk, 1987, pp. 132–157.

    Google Scholar 

  11. Wright J. D. M., “Stone-algebra-valued measures and integrals,” Proc. London Math. Soc., 19, No. 1, 107–122 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  12. Horn A. and Tarski A., “Measures in Boolean algebras,” Trans. Amer. Math. Soc., 64, No. 3, 467–497 (1948).

    Article  MathSciNet  MATH  Google Scholar 

  13. Los J. and Marczewski E., “Extensions of measure,” Fund. Math., 36, 267–276 (1949).

    MathSciNet  MATH  Google Scholar 

  14. Wright J. D. M., “The measure extension procedure for vector lattices,” Ann. Inst. Fourier Grenoble, 21, No. 4, 65–85 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  15. Panchapagesan T. V. and Palled Sh. V., “On vector lattice-valued measures. I,” Math. Slovaca, 33, No. 3, 269–292 (1983).

    MathSciNet  MATH  Google Scholar 

  16. Riecan J., “On the Kolmogorov consistency theorem for Riesz space valued measures,” Acta Math. Univ. Comen., 48/49, 173–180 (1986).

    MathSciNet  Google Scholar 

  17. Wright J. D. M., “Vector lattice measures on locally compact spaces,” Math. Z., 120, No. 3, 193–203 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  18. Kasch F., Modules and Rings, Academic Press, London and New York (1982).

    MATH  Google Scholar 

  19. Wright J. D. M., “Products of positive vector measures,” Quart. J. Math., 24, No. 94, 189–206 (1973).

    Article  MATH  Google Scholar 

  20. Duchon M. and Kluvanek I., “Inductive tensor product of vector valued measures,” Mat. Casop., 17, No. 2, 108–112 (1967).

    MathSciNet  MATH  Google Scholar 

  21. Duchon M., “On the projective tensor product of vector valued measures,” Mat. Casop., 17, No. 2, 113–120 (1967).

    MathSciNet  MATH  Google Scholar 

  22. Kluvanek I., “On the product of vector measures,” J. Austral. Math. Soc., 15, No. 1, 22–26 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  23. Akhiezer N. I., The Classical Moment Problem and Some Related Topics in Analysis, Oliver & Boyd, Edinburgh and London (1965).

    Google Scholar 

  24. Kreĭn M. G. and Nudel’man A. A., The Markov Moment Problem and Extremal Problems: Ideas and Problems of P. L. Chebyshëv and A. A. Markov and Their Further Development, American Mathematical Society, Providence (1977).

    Google Scholar 

  25. Niåstad O., “Unique solvability of an extended Hamburger moment problem,” J. Math. Anal. Appl., 124, No. 2, 502–519 (1987).

    Article  MathSciNet  Google Scholar 

  26. Alden E., On Indeterminacy of Strong Moment Problems [Preprint/Univ. Umea; No. 2], Sweden (1988).

    Google Scholar 

  27. Shonkwiler R., “On the solution of moment problems by reproducing kernel methods,” J. Math. Anal. Appl., 130, No. 1, 271–299 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  28. F. Riesz and B. Szökefalvi-Nagy, Functional Analysis, Dover Publications, New York (1990).

    MATH  Google Scholar 

  29. Vorob’ëv Yu. V., “Orthogonal operator polynomials and approximate methods for determining spectra of bounded linear operators,” Uspekhi Mat. Nauk, 9, No. 1, 83–90 (1954).

    MATH  Google Scholar 

  30. Berezanskii Yu. M., “The generalized power moment problem,” Trudy Moskovsk. Mat. Obshch., 21, 47–102 (1970).

    MathSciNet  Google Scholar 

  31. Sebestyen Z., “Moment theorems for operators on Hilbert spaces,” Acta Sci. Math. Szegel., 47, No. 1–2, 101–106 (1984).

    MathSciNet  MATH  Google Scholar 

  32. Schmüdgen K., “On a generalization of the classical moment problem,” J. Math. Anal. Appl., 125, No. 2, 461–470 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  33. Khurana S. S., “Lattice-valued Borel measures,” Rocky Mount. J. Math., 6, No. 2, 377–382 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  34. Malyugin S. A., “Quasi-Radon measures,” Sibirsk. Mat. Zh., 32, No. 5, 103–111 (1991).

    MathSciNet  Google Scholar 

  35. Malyugin S. A., “On the vector Hamburger moment problem,” Optimization, No. 48, 124–141 (1990).

    Google Scholar 

  36. Krein M. G., “Infinite J-matrices and the matrix moment problem,” Dokl. Akad. Nauk SSSR, 69, No. 2, 125–128 (1949).

    MathSciNet  MATH  Google Scholar 

  37. Berezanskii Yu. M., Expansions in Eigenfunctions of Selfadjoint Operators, American Mathematical Society, Providence (1968).

    MATH  Google Scholar 

  38. Sz.-Nagy B., “A moment problem for self-adjoint operators,” Acta Math. Acad. Sci. Hung., 3, 285–293 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  39. Hewitt E. and Ross K., Abstract Harmonic Analysis. Vol. 1 and 2, Springer-Verlag, New York (1994).

    Book  Google Scholar 

  40. Naĭmark M. A., Normed Rings, McGraw-Hill Book Co., New York (1973).

    Google Scholar 

  41. Heyer H., Probability Measures on Locally Compact Groups, Springer-Verlag, Berlin etc. (1977).

    Book  MATH  Google Scholar 

  42. Takeuti G., “A transfer principle in harmonic analysis,” J. Symbolic Logic, 44, No. 3, 417–440 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  43. Loomis L. H., An Introduction to Abstract Harmonic Analysis, D. Van Nostrand Company Inc., Princeton (1953).

    MATH  Google Scholar 

  44. Sarymsakov T. A., Ayupov Sh. A., Khadziev Dzh., and Chilin V. I., Ordered Algebras [in Russian], Fan, Tashkent (1983).

    Google Scholar 

  45. Christensen M. J., “Extension theorems for operator-valued measures,” J. Math. Phys., 20, No. 3, 385–389 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  46. Rudin W., Functional Analysis, McGraw-Hill Book Co., New York (1973).

    MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Kusraev, A.G., Malyugin, S.A. (2000). Vector Measures and Dominated Mappings. In: Kutateladze, S.S. (eds) Nonstandard Analysis and Vector Lattices. Mathematics and Its Applications, vol 525. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4305-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4305-9_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5863-6

  • Online ISBN: 978-94-011-4305-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics