A note on sequences lying in the range of a vector measure valued in the bidual

Marchena, Begoña; Piñeiro, Cándido

doi:10.1090/S0002-9939-98-04350-0

A note on sequences lying in the range of a vector measure valued in the bidual
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by Begoña Marchena and Cándido Piñeiro PDF

Proc. Amer. Math. Soc. 126 (1998), 3013-3017 Request permission

Abstract:

Let $X$ be a Banach space. It is unknown if every subset $A$ of $X$ lying in the range of an $X^{**}$-valued measure is actually contained in the range of an $X$-valued measure. In this paper we solve this problem in the case when we consider only vector measures of bounded variation.

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