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Winter 2002 The McShane and the Pettis integral of Banach space-valued functions defined on ${\Bbb R}\sp m$
Štefan Schwabik, Guoju Ye
Illinois J. Math. 46(4): 1125-1144 (Winter 2002). DOI: 10.1215/ijm/1258138470

Abstract

In this paper, we define and study the McShane integral of functions mapping a compact interval $I_0$ in $R^m$ into a Banach space $X$. We compare this integral with the Pettis integral and prove, in particular, that the two integrals are equivalent if $X$ is reflexive and the unit ball of the dual $X^*$ satisfies an additional condition (P). This gives additional information on an implicitly stated open problem of R.A. Gordon and on the work of D.H. Fremlin and J. Mendoza.

Citation

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Štefan Schwabik. Guoju Ye. "The McShane and the Pettis integral of Banach space-valued functions defined on ${\Bbb R}\sp m$." Illinois J. Math. 46 (4) 1125 - 1144, Winter 2002. https://doi.org/10.1215/ijm/1258138470

Information

Published: Winter 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1038.28009
MathSciNet: MR1988254
Digital Object Identifier: 10.1215/ijm/1258138470

Subjects:
Primary: 28B05
Secondary: 26A39, 46G10

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 4 • Winter 2002
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