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Title: On the strong McShane integral of functions with values in a Banach space (English)
Author: Schwabik, Štefan
Author: Guoju, Ye
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 51
Issue: 4
Year: 2001
Pages: 819-828
Summary lang: English
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Category: math
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Summary: The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions. (English)
Keyword: Bochner integral
Keyword: strong McShane integral
MSC: 26A39
MSC: 28-02
MSC: 28B05
MSC: 46G10
idZBL: Zbl 1002.28013
idMR: MR1864044
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Date available: 2009-09-24T10:47:27Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/127688
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Reference: [5] J. Kurzweil: Nichtabsolut Konvergente Integrale.BSB B. G.  Teubner Verlagsgesellschaft, Leipzig, 1980. Zbl 0441.28001, MR 0597703
Reference: [6] S. Lang: Real and Functional Analysis.Springer-Verlag, New York, 1993. Zbl 0831.46001, MR 1216137
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Reference: [8] V. A. Skvortsov and A. P. Solodov: A variational integral for Banach-valued functions.Real Anal. Exchange 24 (1998/99), 799–806. MR 1704751
Reference: [9] P.-Y. Lee: Lanzhou Lectures on Henstock Integration.World Scientific, Singapore, 1989. Zbl 0699.26004, MR 1050957
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