On Henstock--Kurzweil and McShane integrals of Banach space-valued functions
type: Item
instance of: scholarly article
title: On Henstock--Kurzweil and McShane integrals of Banach space-valued functions
zbMATH Open document ID: 1160.46028
author: Guoju Ye
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-05-04T00:00:00Z
review text: The problem of Henstock--Kurzweil integration of Banach space valued functions is studied with the aim to derive an analogue of a known result for the Perron integral of real functions saying that every Perron integrable function is such that every portion of the integration domain contains an interval on which the function is Lebesgue integrable. It turns out that such results hold for the case when the Banach space does not contain an isomorphic copy of the space \(c_0\). The McShane integral replaces the Lebesgue integral for infinite-dimensional Banach spaces. Various variants of results of this type are given in the paper.
reviewed by: Štefan Schwabik
Mathematics Subject Classification ID: 46G10
zbMATH DE Number: 5149490
zbMATH Keywords: Henstock-Kurzweil integral
zbMATH Keywords: McShane integral
zbMATH Keywords: Pettis integral
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.08.020
OpenAlex ID: W2062747127
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DOI: 10.1016/J.JMAA.2006.08.020
description: scientific article; zbMATH DE number 5149490