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Proceedings of the American Mathematical Society

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


Authors: Begoña Marchena and Cándido Piñeiro
Journal: Proc. Amer. Math. Soc. 126 (1998), 3013-3017
MSC (1991): Primary 46G10, 47B10
DOI: https://doi.org/10.1090/S0002-9939-98-04350-0
MathSciNet review: 1451819
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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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Additional Information

Begoña Marchena
Affiliation: Departamento de Matemáticas, Escuela Politécnica Superior, Universidad de Huelva, 21810 La Rábida, Huelva, Spain

Cándido Piñeiro
Affiliation: Departamento de Matemáticas, Escuela Politécnica Superior, Universidad de Huelva, 21810 La Rábida, Huelva, Spain
Email: candido@uhu.es

DOI: https://doi.org/10.1090/S0002-9939-98-04350-0
Received by editor(s): October 14, 1996
Received by editor(s) in revised form: March 14, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society