Some peculiarities of the Henstock and Kurzweil integrals of Banach space-valued functions
type: Item
instance of: scholarly article
title: Some peculiarities of the Henstock and Kurzweil integrals of Banach space-valued functions
zbMATH Open document ID: 1069.28006
published in: Real Analysis Exchange
publication date: 2005-03-07T00:00:00Z
review text: In the paper relationships among the spaces of Banach space-valued functions which are Riemann integrable, Riemann-McShane integrable, Bochner integrable, McShane integrable, variationally Henstock integrable or Henstock integrable are investigated. The author presents several nice examples showing that in general the equalities are false. Moreover, a proof (due to C. S. Hoenig) of the equivalence of the Bochner integral and the variational McShane integral is given. This result has been independently proven (by a different method and later) by \textit{C. Wu} and \textit{X. Yao} [J. Math. Stud. 27, No.~1, 32--36 (1994; Zbl 0947.28010)] and -- in a more general setting -- by \textit{L. Di Piazza} and \textit{K. Musiał} [Ill. J. Math. 45, No.~1, 279--289 (2001; Zbl 0999.28006)].
Mathematics Subject Classification ID: 28B05
Mathematics Subject Classification ID: 26A39
Mathematics Subject Classification ID: 26A42
Mathematics Subject Classification ID: 46G10
zbMATH DE Number: 2141362
zbMATH Keywords: Henstock integrals
zbMATH Keywords: Kurzweil integrals
zbMATH Keywords: Banach space-valued functions
author: M. Federson
reviewed by: Kazimierz Musial
MaRDI profile type: Publication
OpenAlex ID: W1521258777
DOI: 10.14321/REALANALEXCH.29.1.0439
description: scientific article; zbMATH DE number 2141362