An integral on a complete metric measure space

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Abstract

We study a Henstock-Kurzweil type integral defined on a complete metric measure space XX endowed with a Radon measure μμ and with a family of “cells” FF that satisfies the Vitali covering theorem with respect to μμ. 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 ss-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∗ACG∗ functions (Main Theorem 1) and in terms of variational measures (Main Theorem 2).
Lingua originaleEnglish
pagine (da-a)157-178
Numero di pagine22
RivistaReal Analysis Exchange
Volume40
Stato di pubblicazionePublished - 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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