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Title: Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions (English)
Author: Bongiorno, B.
Author: Di Piazza, Luisa
Author: Musiał, K.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 131
Issue: 2
Year: 2006
Pages: 211-223
Summary lang: English
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Category: math
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Summary: We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by $\sum _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ belong to a Banach space and the sets $E_n$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for the Bochner and for the Pettis integrability of $f$ (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions. (English)
Keyword: Kurzweil-Henstock integral
Keyword: Kurzweil-Henstock-Pettis integral
Keyword: Pettis integral
MSC: 26A39
MSC: 26A42
MSC: 26A45
MSC: 28B05
idZBL: Zbl 1112.26015
idMR: MR2242846
DOI: 10.21136/MB.2006.134086
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Date available: 2009-09-24T22:25:49Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/134086
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Reference: [2] B. Bongiorno: The Henstock-Kurzweil integral.Handbook of Measure Theory I, E. Pap ed., Elsevier Amsterdam, 2002, pp. 587–615. Zbl 1024.26004, MR 1954623
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Reference: [4] D. H. J. Fremlin: The Henstock and McShane integrals of vector-valued functions.Illinois J. Math. 38 (1994), 471–479. Zbl 0797.28006, MR 1269699, 10.1215/ijm/1255986726
Reference: [5] J. L. Gamez, J. Mendoza: On Denjoy-Dunford and Denjoy-Pettis integrals.Studia Math. 130 (1998), 115–133. MR 1623348
Reference: [6] P. Y. Lee: Lanzhou Lectures on Henstock Integration.World Scientific, Singapore, 1989. Zbl 0699.26004, MR 1050957
Reference: [7] K. Musial: Topics in the theory of Pettis integration.Rend. Istit. Mat. Univ. Trieste 23 (1991), 177–262. Zbl 0798.46042, MR 1248654
Reference: [8] C. Swartz: Norm convergence and uniform integrability for the Kurzweil-Henstock integral.Real Anal. Exchange 24 (1998/99), 423–426. MR 1691761
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