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Title: Henstock-Kurzweil and McShane product integration; descriptive definitions (English)
Author: Slavík, Antonín
Author: Schwabik, Štefan
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 1
Year: 2008
Pages: 241-269
Summary lang: English
Category: math
Summary: The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function $A$ is absolutely continuous. As a consequence we obtain that the McShane product integral of $A$ over $[a,b]$ exists and is invertible if and only if $A$ is Bochner integrable on $[a,b]$. (English)
Keyword: Henstock-Kurzweil product integral
Keyword: McShane product integral
Keyword: Bochner product integral
MSC: 26A39
MSC: 28B05
MSC: 46G10
idZBL: Zbl 1174.28013
idMR: MR2402536
Date available: 2009-09-24T11:54:41Z
Last updated: 2016-04-07
Stable URL:
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