The Denjoy-type definition of \(B\)-integral
type: Item
instance of: scholarly article
zbMATH Open document ID: 0979.26004
author: Guoju Ye
author: Tianqing An
publication date: 2002-02-19T00:00:00Z
Mathematics Subject Classification ID: 26B99
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 1616532
zbMATH Keywords: Henstock integral
zbMATH Keywords: \(B\)-integral
zbMATH Keywords: Vitali covers
zbMATH Keywords: variational integral
zbMATH Keywords: Denjoy integral
zbMATH Keywords: regularity of an interval
MaRDI profile type: Publication
title: The Denjoy-type definition of \(B\)-integral
published in: Acta Mathematica Scientia. Series A. (Chinese Edition)
review text: Let \(B\) be a collection of Vitali covers of an interval in the \(n\)-dimensional space with filtering and complete properties, but without partition property. Then the multidimensional Henstock variational integral can be defined using \(B\). In this short note, a corresponding Denjoy integral is given. However, intervals used in the integral are regular. Since the regularity of an interval is not a hereditary property, the integrability over an interval does not imply that over all subintervals.
reviewed by: Tuan Seng Chew
description: scientific article; zbMATH DE number 1616532