Nearly upper semicontinuous gauge functions in \({\mathbb{R}}^ m\)
type: Item
instance of: scholarly article
title: Nearly upper semicontinuous gauge functions in \({\mathbb{R}}^ m\)
zbMATH Open document ID: 0656.26008
published in: Real Analysis Exchange
publication date: 1988-01-01T00:00:00Z
review text: The basic result of this paper is that in defining generalized Riemann integrals by the method of Henstock-Kurzweil it suffices that the gauge function be upper semicontinuous on the complement of a set of measure zero (in particular we can assume the gauge is measurable). This result is due to Pfeffer but his proof uses methods valid in one dimension only. The present author gives a proof that translates easily to higher dimensions. It is known that the gauge function need not be upper semicontinuous everywhere [\textit{J. Foran} and \textit{S. Meinershagen}, Real Anal. Exch. 13(1987/88), 265-277 (1988)].
Mathematics Subject Classification ID: 26A39
Mathematics Subject Classification ID: 26B99
zbMATH DE Number: 4071248
zbMATH Keywords: higher dimensional Henstock-Kurzweil integral
zbMATH Keywords: Denjoy-Perron integral
zbMATH Keywords: generalized Riemann integrals
zbMATH Keywords: gauge function
author: Zoltán Buczolich
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4071248