This article is cited in 10 papers

Theorem of Bartle, Dunford, and Schwartz concerning vector measures

V. I. Rybakov

Shuiskii Pedagogical Institute

Abstract: We show the existence, for an arbitrary vector measure $\mu:\Sigma\to X$ (where $X$ is a Banach space and $\Sigma$ is a $\sigma$-algebra of subsets of a set $S$) of a functional $x'\in X'$ ($X'$ is the conjugate space of $X$) such that $\mu$ is absolutely continuous with respect to $\mu_{x'}$, $\mu_{x'}(E)=<x', \mu(E)>$, $E\in\Sigma$.

UDC: 513.83

Received: 27.01.1969

 English version: Mathematical Notes, 1970, 7:2, 147–151

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