This article is cited in 3 papers

Pettis integrability of Stone transforms

V. I. Rybakov

Tula State Pedagogical University

Abstract: Let $f$ be a bounded Pettis integrable function ranging in a Banach space $X$ (the range of the indefinite Pettis integral is separable). We consider Pettis integrability conditions for the Stone transform of $f$ and relate this problem to the regular oscillation condition for the family of functions $\{x^*f:x^*\in B(X^*)\}$, where $B(X^*)$ is the unit ball in $X^*$.

UDC: 517.98

Received: 20.02.1995

DOI: 10.4213/mzm1822

 English version: Mathematical Notes, 1996, 60:2, 175–185

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