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Spring 2009 A variational Henstock integral characterization of the Radon–Nikodým property
B. Bongiorno, L. Di Piazza, K. Musiał
Illinois J. Math. 53(1): 87-99 (Spring 2009). DOI: 10.1215/ijm/1264170840

Abstract

A characterization of Banach spaces possessing the Radon–Nikodým property is given in terms of finitely additive interval functions. We prove that a Banach space $X$ has the RNP if and only if each $X$-valued finitely additive interval function possessing absolutely continuous variational measure is a variational Henstock integral of an $X$-valued function. Due to that characterization several $X$-valued set functions that are only finitely additive can be represented as integrals.

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B. Bongiorno. L. Di Piazza. K. Musiał. "A variational Henstock integral characterization of the Radon–Nikodým property." Illinois J. Math. 53 (1) 87 - 99, Spring 2009. https://doi.org/10.1215/ijm/1264170840

Information

Published: Spring 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1200.46021
MathSciNet: MR2584936
Digital Object Identifier: 10.1215/ijm/1264170840

Subjects:
Primary: 26A39 , 28B05 , 46G05 , 46G10 , 58C20

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

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Vol.53 • No. 1 • Spring 2009
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