Comparison between different types of abstract integrals in Riesz spaces
type: Item
instance of: scholarly article
title: Comparison between different types of abstract integrals in Riesz spaces
zbMATH Open document ID: 0881.28008
DOI: 10.1007/BF02977030
author: A. Boccuto
author: A. R. Sambucini
publication date: 1998-02-17T00:00:00Z
review text: Let \(E\) be a Dedekind complete Riesz space and \([a,b]\) a real interval. In the first part of the paper, the authors give a characterization of ``Riemann-integrable'' functions \(f:[a,b]\to E\) well known in the real-valued case. In the second part, they introduce an integral for real-valued functions with respect to an \(E\)-valued measure: A function \(f\) is integrable if there is an \(L^1\)-Cauchy sequence of simple functions \((o)\)-converging in measure to \(f\). This concept of integrability is compared with several other concepts of integrability.
Mathematics Subject Classification ID: 28B15
zbMATH DE Number: 1057437
zbMATH Keywords: Dedekind complete Riesz space
zbMATH Keywords: concept of integrability
reviewed by: Hans Weber
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02977030
OpenAlex ID: W1967327481
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1057437