Mathematical Notes

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

Pettis integrability of Stone transforms

  • V. I. Rybakov


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 


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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

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

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