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2013/2014 An Integral on a Complete Metric Measure Space
Donatella Bongiorno, Giuseppa Corrao
Real Anal. Exchange 40(1): 157-178 (2013/2014).


We study a Henstock-Kurzweil type integral defined on a complete metric measure space \(X\) endowed with a Radon measure \(\mu\) and with a family of “cells” \(\mathcal{F}\) that satisfies the Vitali covering theorem with respect to \(\mu\). This integral encloses, in particular, the classical Henstock-Kurzweil integral on the real line, the dyadic Henstock-Kurzweil integral, the Mawhin’s integral [19], and the \(s\)-HK integral [4]. The main result of this paper is the extension of the usual descriptive characterizations of the Henstock-Kurzweil integral on the real line, in terms of \(ACG^*\) functions (Main Theorem 1) and in terms of variational measures (Main Theorem 2).


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Donatella Bongiorno. Giuseppa Corrao. "An Integral on a Complete Metric Measure Space." Real Anal. Exchange 40 (1) 157 - 178, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 1 July 2015

zbMATH: 06848829
MathSciNet: MR3365396

Primary: 26A39 ,
Secondary: 28A12

Keywords: \(ACG^\bigtriangleup\) function , critical variation , HK-integral

Rights: Copyright © 2015 Michigan State University Press

Vol.40 • No. 1 • 2013/2014
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