Mathematical Notes

, Volume 60, Issue 2, pp 175–185 | Cite as

Pettis integrability of Stone transforms

  • V. I. Rybakov
Article
  • 28 Downloads

Abstract

Letf be a bounded Pettis integrable function ranging in a Banach spaceX (the range of the indefinite Pettis integral is separable). We consider Pettis integrability conditions for the Stone transform off and relate this problem to the regular oscillation condition for the family of functions {x*f∶x*∈B(X*)}, whereB(X*) is the unit ball inX*.

Key words

Pettis integrability Stone transformation regular oscillation condition Banach space Borel measurability perfect measure Radon measure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Talangrand, “Pettis integral and measure theory,”Amer. Math. Soc. Memoirs,307 (1984).Google Scholar
  2. 2.
    D. Sentilles and R. Wheeler, “Pettis integration via the Stonian transform,”Pacific J. Math.,107, No. 2, 473–495 (1983).MathSciNetGoogle Scholar
  3. 3.
    V. V. Sazonov, “Perfect measures,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],26, No.3, 391–414 (1962).MATHMathSciNetGoogle Scholar
  4. 4.
    D. Flemlin and M. Talagrand, “A decomposition theorem for additive set-functions, with applications to Pettis integrals and ergodic means,”Math. Z.,168, 117–142 (1979).MathSciNetGoogle Scholar
  5. 5.
    N. Ghoussoub, G. Godefroy, B. Maurey, and W. Schachermayer, “Some topological and geometrical structures in Banach spaces,”Amer. Math. Soc. Memoirs,378 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. I. Rybakov
    • 1
  1. 1.Tula State Pedagogical UniversityUSSR

Personalised recommendations