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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Boundedness of vector measures with values in the spaces $ L\sb{0}$ of Bochner measurable functions


Author: Lech Drewnowski
Journal: Proc. Amer. Math. Soc. 91 (1984), 581-588
MSC: Primary 46G10; Secondary 28B05, 46E40
MathSciNet review: 746094
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Abstract: Let $ {L_0}(Z)$ be the $ F$-space of all Bochner measurable functions from a probability space to a Banach space $ Z$. We prove that every countably additive vector measure taking values in $ {L_0}(Z)$ has bounded range. This generalizes a recent result due to M. Talagrand and, independently, N. J. Kalton, N. T. Peck and J. W. Roberts, asserting the same for the case when $ Z$ is the space of scalars.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746094-6
PII: S 0002-9939(1984)0746094-6
Keywords: Vector measures, bounded range, Bochner measurable functions
Article copyright: © Copyright 1984 American Mathematical Society