Riemann integration in Banach spaces
type: Item
instance of: scholarly article
title: Riemann integration in Banach spaces
zbMATH Open document ID: 0764.28008
author: Russell A. Gordon
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-04-01T00:00:00Z
review text: This paper contains a clear and interesting exposition of several questions related with the Riemann integration of functions mapping (bounded) closed intervals into Banach spaces. One of the main focuses of the paper is to analyse the Banach spaces having the property of Lebesgue (i.e., those spaces having the property that every Riemann integrable function is continuous almost everywhere on the interval). Also it is examined the relationship between the Riemann integral (in Banach spaces) and other (vector-valued) integrals. Most of the results in this paper are a compilation of works of Graves, Alexiewicz and Orlicz, Rejouani, Nemirovski, Ochan and Rejouani, and da Rocha. Some of the proves presented here are simpler than the original ones.
Mathematics Subject Classification ID: 28B05
Mathematics Subject Classification ID: 46G10
zbMATH DE Number: 150388
zbMATH Keywords: measurable function
zbMATH Keywords: vector-valued integral
zbMATH Keywords: Riemann integral
zbMATH Keywords: Banach spaces
reviewed by: P. Jiménez Guerra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072923
OpenAlex ID: W1997415713
cites work: Remarks on Riemann-integration of vector-valued functions
cites work: Tsirelson's space. With an appendix by J. Baker, O. Slotterbeck and R. Aron
cites work: Q4148368
cites work: Super-reflexive spaces with bases
cites work: Q4136031
cites work: On Integration in Vector Spaces
cites work: Q5630185
cites work: Q5635867
DOI: 10.1216/RMJM/1181072923
description: scientific article; zbMATH DE number 150388