Skip to main content

The Radon-Nikodým theorem for vector measures

Part of the Lecture Notes in Mathematics book series (LNM,volume 485)

Keywords

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

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, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Birkhoff, Integration of functions with values in a Banach space, Trans. AMS, 38 (1935), 357–378.

    MathSciNet  MATH  Google Scholar 

  2. S. Bochner, Integration von Funkionen, deren Werte die Elemente eines Vectorraumes sind, Fund. Math., 20 (1933), 262–276.

    MATH  Google Scholar 

  3. S. D. Chatterji, Martingale convergence and the Radon-Nikodym theorem in Banach spaces, Math. Scand., 22 (1968), 21–41.

    MathSciNet  MATH  Google Scholar 

  4. J. A. Clarkson, Uniformly convex spaces, Trans. AMS, 40 (1936), 396–414.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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. J. Diestel and B. Faires, On vector measures, Trans. AMS., 198 (1974), 253–271.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. J Diestel and J. J. Uhl, Jr., The Radon-Nikodým Theorem for Banach Space Valued Measures, Rocky Mtn. Journ.

    Google Scholar 

  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. N. Dunford and M. Morse, Remarks on the preceding paper of James A. Clarkson, Trans. AMS, 40 (1936), 415–420.

    MathSciNet  MATH  Google Scholar 

  10. N. Dunford and B. J. Pettis, Linear operations on summable functions, Trans. AMS., 47 (1940), 323–392.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. G. A. Edgar, A non-compact Choquet theorem, Proc. AMS.

    Google Scholar 

  12. I. M. Gelfand, Abstrakte Funtionen und lineare Operatoren, Mat. Sbornik N.S., 4(46) (1938), 235–286.

    MATH  Google Scholar 

  13. E. Hille and R. S. Phillips, Functional Analysis and Semigroups. AMS Colloquium, Providence, RI, 1957.

    Google Scholar 

  14. R. E. Huff, Dentability and the Radon-Nikodým property, Duke Math. J., 41 (1974), 111–114.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. R. E. Huff and P. Morris, Dual spaces with the Krein-Milman property have the Radon-Nikodým property, Proc. AMS.

    Google Scholar 

  16. R. E. Huff and P. Morris, Geometric characterizations of the Radon-Nikodým property in Banach spaces.

    Google Scholar 

  17. S. S. Khurana, Barycenters, extreme points and strongly extreme points, Math. Am. 198 (1972), 81–84.

    MathSciNet  MATH  Google Scholar 

  18. S. S. Khurana, Barycenters, pinnacle points and denting points, Trans. AMS, 180 (1973), 497–503.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. T. Kuo, Grothendieck spaces and dual spaces possessing the Radon-Nikodým property. Ph. D. thesis (Carnegie-Mellon University), 1974.

    Google Scholar 

  20. E. Leonard and K. Sundaresan, Smoothness in Lebesgue-Bochner function spaces and the Radon-Nikodým theorem, to appear.

    Google Scholar 

  21. J. Lindenstrauss, On extreme points in ℓ1, Israel J. Math., 41 (1966), 59–61.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. H. Maynard, A geometric characterization of Banach spaces possessing the Radon-Nikodym theorem, Trans. AMS, 185 (1973), 493–500.

    CrossRef  MathSciNet  Google Scholar 

  23. M. Metivier, Martingales a valears vectorielles. Applications a la derivations des mesures vectorielles, Ann. Inst. Fourier (Grenoble), 17 (1967), 175–208.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. S. Moedomo and J. J. Uhl, Jr., Radon-Nikodym theorems for the Bochner and Pettis integrals, Pacific Journal Math., 38 (1971), 531–536.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. I. Namioka, Neighborhoods of extreme points, Israel J. Math., 5 (1967), 145–152.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc., 44 (1938), 277–304.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. R. R. Phelps, Dentability and extreme points in Banach spaces, J. of Functional Analysis, 16 (1974), 78–90.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc., 48 (1940), 516–541.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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. M. A. Rieffel, The Radon-Nikodým theorem for the Bochner integral, Trans. AMS, 131 (1968), 466–487.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. H. P. Rosenthal, On injective Banach spaces and the spaces L (μ) for finite measures μ, Acta Math, 124 (1970), 205–248.

    CrossRef  MathSciNet  Google Scholar 

  32. C. Stegall, The Radon-Nikodým property in conjugate Banach spaces, Trans. AMS.

    Google Scholar 

  33. J. J. Uhl, Jr., A note on the Radon-Nikodým property for Banach spaces, Revue Roum. Math., 17 (1972), 113–115.

    MathSciNet  MATH  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1975 Springer-Verlag

About this chapter

Cite this chapter

Diestel, J. (1975). The Radon-Nikodým theorem for vector measures. In: Geometry of Banach Spaces-Selected Topics. Lecture Notes in Mathematics, vol 485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082085

Download citation

  • DOI: https://doi.org/10.1007/BFb0082085

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07402-1

  • Online ISBN: 978-3-540-37913-3

  • eBook Packages: Springer Book Archive