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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some remarks on the average range of a vector measure


Author: Francisco J. Freniche
Journal: Proc. Amer. Math. Soc. 107 (1989), 119-124
MSC: Primary 46G10; Secondary 28B05
DOI: https://doi.org/10.1090/S0002-9939-1989-0962243-3
MathSciNet review: 962243
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Abstract: We study some conditions on the average range of a vector measure with values in the bidual of a Banach space which imply that the range is contained in the space. We prove that Geitz's condition is a sufficient one if the dual closed unit ball is weak-star sequentially compact. We also show how to reduce to measures with values in the bidual of $ {l^\infty }$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0962243-3
Keywords: Weakly convergent sequences in $ {L^1}$, Pettis integral, core of a vector measure
Article copyright: © Copyright 1989 American Mathematical Society