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The Radon-Nikodým theorem for vector measures

  • Joseph Diestel
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 485)

Keywords

Banach Space Extreme Point Convex Subset Polish Space Continuous Linear Operator 
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References

  1. [1]
    G. Birkhoff, Integration of functions with values in a Banach space, Trans. AMS, 38 (1935), 357–378.MathSciNetzbMATHGoogle Scholar
  2. [2]
    S. Bochner, Integration von Funkionen, deren Werte die Elemente eines Vectorraumes sind, Fund. Math., 20 (1933), 262–276.zbMATHGoogle Scholar
  3. [3]
    S. D. Chatterji, Martingale convergence and the Radon-Nikodym theorem in Banach spaces, Math. Scand., 22 (1968), 21–41.MathSciNetzbMATHGoogle Scholar
  4. [4]
    J. A. Clarkson, Uniformly convex spaces, Trans. AMS, 40 (1936), 396–414.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    W. J. Davis and R. R. Phelps, The Radon-Nikodym property and dentable sets in Banach spaces, Proc. AMS, 45 (1974).Google Scholar
  6. [6]
    J. Diestel and B. Faires, On vector measures, Trans. AMS., 198 (1974), 253–271.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J Diestel and J. J. Uhl, Jr., The Radon-Nikodým Theorem for Banach Space Valued Measures, Rocky Mtn. Journ.Google Scholar
  8. [8]
    J. Diestel and J. J. Uhl, Jr., Topics in the Theory of Vector Measures, Notes presently being collected at Kent State University and the University of Illinois.Google Scholar
  9. [9]
    N. Dunford and M. Morse, Remarks on the preceding paper of James A. Clarkson, Trans. AMS, 40 (1936), 415–420.MathSciNetzbMATHGoogle Scholar
  10. [10]
    N. Dunford and B. J. Pettis, Linear operations on summable functions, Trans. AMS., 47 (1940), 323–392.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    G. A. Edgar, A non-compact Choquet theorem, Proc. AMS.Google Scholar
  12. [12]
    I. M. Gelfand, Abstrakte Funtionen und lineare Operatoren, Mat. Sbornik N.S., 4(46) (1938), 235–286.zbMATHGoogle Scholar
  13. [13]
    E. Hille and R. S. Phillips, Functional Analysis and Semigroups. AMS Colloquium, Providence, RI, 1957.Google Scholar
  14. [14]
    R. E. Huff, Dentability and the Radon-Nikodým property, Duke Math. J., 41 (1974), 111–114.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    R. E. Huff and P. Morris, Dual spaces with the Krein-Milman property have the Radon-Nikodým property, Proc. AMS.Google Scholar
  16. [16]
    R. E. Huff and P. Morris, Geometric characterizations of the Radon-Nikodým property in Banach spaces.Google Scholar
  17. [17]
    S. S. Khurana, Barycenters, extreme points and strongly extreme points, Math. Am. 198 (1972), 81–84.MathSciNetzbMATHGoogle Scholar
  18. [18]
    S. S. Khurana, Barycenters, pinnacle points and denting points, Trans. AMS, 180 (1973), 497–503.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    T. Kuo, Grothendieck spaces and dual spaces possessing the Radon-Nikodým property. Ph. D. thesis (Carnegie-Mellon University), 1974.Google Scholar
  20. [20]
    E. Leonard and K. Sundaresan, Smoothness in Lebesgue-Bochner function spaces and the Radon-Nikodým theorem, to appear.Google Scholar
  21. [21]
    J. Lindenstrauss, On extreme points in ℓ1, Israel J. Math., 41 (1966), 59–61.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    H. Maynard, A geometric characterization of Banach spaces possessing the Radon-Nikodym theorem, Trans. AMS, 185 (1973), 493–500.MathSciNetCrossRefGoogle Scholar
  23. [23]
    M. Metivier, Martingales a valears vectorielles. Applications a la derivations des mesures vectorielles, Ann. Inst. Fourier (Grenoble), 17 (1967), 175–208.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    S. Moedomo and J. J. Uhl, Jr., Radon-Nikodym theorems for the Bochner and Pettis integrals, Pacific Journal Math., 38 (1971), 531–536.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    I. Namioka, Neighborhoods of extreme points, Israel J. Math., 5 (1967), 145–152.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc., 44 (1938), 277–304.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    R. R. Phelps, Dentability and extreme points in Banach spaces, J. of Functional Analysis, 16 (1974), 78–90.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc., 48 (1940), 516–541.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    M. A. Rieffel, Dentable subsets of Banach spaces with applications to a Radon-Nikodým theorem in Functional Analysis (B. R. Gelbaum, editor) Thompson Book Co., Washington, 1967.Google Scholar
  30. [30]
    M. A. Rieffel, The Radon-Nikodým theorem for the Bochner integral, Trans. AMS, 131 (1968), 466–487.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    H. P. Rosenthal, On injective Banach spaces and the spaces L (μ) for finite measures μ, Acta Math, 124 (1970), 205–248.MathSciNetCrossRefGoogle Scholar
  32. [32]
    C. Stegall, The Radon-Nikodým property in conjugate Banach spaces, Trans. AMS.Google Scholar
  33. [33]
    J. J. Uhl, Jr., A note on the Radon-Nikodým property for Banach spaces, Revue Roum. Math., 17 (1972), 113–115.MathSciNetzbMATHGoogle Scholar

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© Springer-Verlag 1975

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  • Joseph Diestel

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