A note on a Pettis-Kurzweil-Henstock type integral in Riesz spaces.
type: Item
instance of: scholarly article
title: A note on a Pettis-Kurzweil-Henstock type integral in Riesz spaces.
zbMATH Open document ID: 1067.28008
author: A. Boccuto
author: Beloslav Riečan
published in: Real Analysis Exchange
publication date: 2004-08-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rae/1150118728
review text: Let \(R\) be a Dedekind complete Riesz space such that the space \(R^*\) of its order continuous functionals separates the points of \(R\). Let \(X\) be a Hausdorff compact topological space and \(f: X\to R\). In this paper, a Pettis-Kurzweil-Henstock type integral of \(f\) on a compact subset is defined. The connection between improper integrals and integrals on compact subsets is discussed and some convergence theorems are also proved.
Mathematics Subject Classification ID: 28B05
Mathematics Subject Classification ID: 26A39
Mathematics Subject Classification ID: 28B10
Mathematics Subject Classification ID: 28B15
Mathematics Subject Classification ID: 46G10
zbMATH DE Number: 2084027
zbMATH Keywords: Pettis integral
zbMATH Keywords: Kurzweil-Henstock integral
zbMATH Keywords: Dedekind complete Riesz space
reviewed by: Tuan Seng Chew
MaRDI profile type: Publication
OpenAlex ID: W1595825051
DOI: 10.14321/REALANALEXCH.28.1.0153
description: scientific article; zbMATH DE number 2084027