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2003-2004 On McShane integrability of Banach space-valued functions.
Jaroslav Kurzweil, Štefan Schwabik
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Real Anal. Exchange 29(2): 763-780 (2003-2004).


The McShane integral of Banach space-valued functions $f:I\to X$ defined on an $m$-dimensional interval $I$ is considered in this paper. We show that a McShane integrable function is integrable over measurable sets contained in $I$ (Theorem 9). A certain type of absolute continuity of the indefinite McShane integral with respect to Lebesgue measure is derived (Theorem 11) and we show that the indefinite McShane integral is countably additive (Theorem 16). Allowing more general partitions using measurable sets instead of intervals another McShane type integral is defined and we show that it is equivalent to the original McShane integral (Theorem 21)


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Jaroslav Kurzweil. Štefan Schwabik. "On McShane integrability of Banach space-valued functions.." Real Anal. Exchange 29 (2) 763 - 780, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1078.28007
MathSciNet: MR2083811

Primary: 26A39 , 28B05 , 46G10

Keywords: McShane integral , vector integration

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
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