This article is cited in 3 papers

The separation from a vector measure of the part representable by a Bochner integral

V. I. Rybakov

Tula Pedagogical University

Abstract: In this paper, the possibility is established of decomposing a vector measure of $\sigma$-finite variation into parts. One of them belongs to the class of vector measures representable by separable-valued weakly integrable functions (in the case of a vector measure of finite variation this part is representable by a Bochner integral); the other part cannot have such a representation on any subset of positive measure of the carrier.
Some properties of measures of these classes are investigated.

UDC: 517

Received: 27.04.1973

 English version: Mathematical Notes, 1975, 17:5, 476–482

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