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On the atomic structure and the range of partially ordered convex cone-valued measures

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Measure Theory and its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1033))

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References

  1. E. M. ALFSEN: Compact Convex Sets and Boundary Integrals. Springer-Verlag, Berlin-Heidelberg-New York, (1971).

    Book  MATH  Google Scholar 

  2. P. CAPEK: Decomposition Theorems in Measure Theory. Math. Slovaca, 31, (1), 53–69, (1981).

    MathSciNet  MATH  Google Scholar 

  3. C. CONSTANTINESCU: Atoms of Group Valued-Measures. Comment. Math. Helvetici, 51, 191–205, (1976).

    Article  MathSciNet  MATH  Google Scholar 

  4. —: The Range of Atomless Group-Valued Measures. Comment. Math. Helvetici, 51, 207–213, (1976).

    Article  MathSciNet  MATH  Google Scholar 

  5. N. DUNFORD and J. SCHWARTZ: Linear Operators, Part I. Interscience, New York, (1958).

    MATH  Google Scholar 

  6. J. DIESTEL and J. J UHL, Jr.: Vector Measures. Math. Surveys No. 15, Amer. Math. Soc., Providence, (1977).

    MATH  Google Scholar 

  7. W. HACKENBROCH: Zum Radon-Nikodymschen Satz für positive Vector-masse. Math. Ann., 206, 63–65, (1973).

    Article  MathSciNet  MATH  Google Scholar 

  8. P. R. HALMOS: The Range of a Vector Measure. Bull. Amer. Math. Soc., 54, 416–421, (1948).

    Article  MathSciNet  MATH  Google Scholar 

  9. J. HOFFMAN-JØRGENSEN: Vector Measures. Math. Scand., 28, 5–32, (1971).

    MathSciNet  MATH  Google Scholar 

  10. R. JOHNSON: Atomic and Nonatomic Measures. Proc. Amer. Math. Soc., 25, 650–655, (1970).

    Article  MathSciNet  MATH  Google Scholar 

  11. D. A. KAPPOS: Probability Algebras and Stochastic Spaces. Acad. Press, (1969).

    Google Scholar 

  12. S. S. KHURANA: Lattice-Valued Borel Measures. Rocky Mountain J. Math., 6, 377–382, (1976).

    Article  MathSciNet  MATH  Google Scholar 

  13. —: Lattice Valued Borel Measures II, Trans. Amer. Math. Soc., 235, 205–211, (1978).

    Article  MathSciNet  MATH  Google Scholar 

  14. I. KLUVANEK and G. KNOWLES: Vector Measures and Control Systems. North Holland, Amsterdam, (1975).

    MATH  Google Scholar 

  15. A. LIAPOUNOV: Sur les fonctions-vecteurs complètement additives. Izv. Akad. Nauk S.S.S.R. Ser. Mat. 4, 465–478, (1940), (Russian).

    MATH  Google Scholar 

  16. K. MUSIAL: Absolute Continuity and the Range of Group-valued Measure. Bull. Acad. Pol. Sci. Sér. Sci. Math. Astr. Phys., 21, 105–113, (1973).

    MathSciNet  MATH  Google Scholar 

  17. P. K. PAVLAKOS: The Lebesgue Decomposition Theorem for Partially Ordered Semigroup-valued Measures. Proc. Amer. Math. Soc., 71, 207–211, (1978).

    Article  MathSciNet  MATH  Google Scholar 

  18. R. R. PHELPS: A Banach Space Characterization of Purely Atomic Measure Spaces. Proc. Amer. Math. Soc., 12, 447–452, (1961).

    Article  MathSciNet  MATH  Google Scholar 

  19. K. SWONG: A Representation Theory of Continuous Linear Maps. Math. Ann., 155, 270–291 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  20. T. TRAYNOR: Decompositions of Group-valued Additive Set Functions. Ann. Inst. Fourier (Grenoble), 22, fasc. 3, 131–140, (1972).

    Article  MathSciNet  MATH  Google Scholar 

  21. B. Z. VULIKH: Introduction to the Theory of Partially Ordered Spaces. Groningen, Wolters-Noordhoff, (1967).

    MATH  Google Scholar 

  22. J. D. M. WRIGHT: Stone-Algebra-Valued Measures and Integrals. Proc. London Math. Soc., 19, 107–122, (1969).

    Article  MathSciNet  MATH  Google Scholar 

  23. —: Measures with Values in a Partially Ordered Vector Space. Proc. London Math. Soc., 25, 675–688, (1972).

    Article  MathSciNet  MATH  Google Scholar 

  24. —: Measures with Values in Partially Ordered Spaces: Regularity and σ-additivity. Measure Theory, Oberwolfach, Lecture Notes in Math., vol. 541, 267–276, (1975).

    Google Scholar 

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Jean-Marc Belley Jacques Dubois Pedro Morales

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© 1983 Springer-Verlag

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Pavlakos, P.K. (1983). On the atomic structure and the range of partially ordered convex cone-valued measures. In: Belley, JM., Dubois, J., Morales, P. (eds) Measure Theory and its Applications. Lecture Notes in Mathematics, vol 1033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099863

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  • DOI: https://doi.org/10.1007/BFb0099863

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12703-1

  • Online ISBN: 978-3-540-38690-2

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