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Mat. Zametki, 1970, Volume 7, Issue 2, Pages 247–254 (Mi mz9502)  

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 $\mu_{x'}$, $\mu_{x'}(E)=<x', \mu(E)>$, $E\in\Sigma$.

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

Bibliographic databases:

UDC: 513.83
Received: 27.01.1969

Citation: V. I. Rybakov, “Theorem of Bartle, Dunford, and Schwartz concerning vector measures”, Mat. Zametki, 7:2 (1970), 247–254; Math. Notes, 7:2 (1970), 147–151

Citation in format AMSBIB
\Bibitem{Ryb70}
\by V.~I.~Rybakov
\paper Theorem of Bartle, Dunford, and Schwartz concerning vector measures
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 2
\pages 247--254
\mathnet{http://mi.mathnet.ru/mz9502}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=260971}
\zmath{https://zbmath.org/?q=an:0198.47801|0193.43203}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 2
\pages 147--151
\crossref{https://doi.org/10.1007/BF01093500}


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