Vol. 91, No. 1, 1980

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A characterization of the local Radon-Nikodým property by tensor products

Donald P. Story

Vol. 91 (1980), No. 1, 219–222

In this paper, results are presented that characterize the collection of all vector valued measures expressible as an indefinite Bochner integral. More precisely, if X is a Banach space, an X-valued vector measure, τ, defined on a measurable space (S,Ω) is expressible as a Bochner integral if and only if τ belongs to ca(S,Ω) πX, where π denotes the strong (or projective) tensor product of two Banach spaces. Other related results are given.

Mathematical Subject Classification 2000
Primary: 46G10
Secondary: 28B05
Received: 8 May 1979
Published: 1 November 1980
Donald P. Story