On singularity of Henstock integrable functions
type: Item
instance of: scholarly article
title: On singularity of Henstock integrable functions
zbMATH Open document ID: 1015.26016
author: Jitan Lu
author: Peng-Yee Lee
published in: Real Analysis Exchange
publication date: 2003-01-05T00:00:00Z
review text: If \(f : [0,1]\to\mathbb R\) is Henstock--Kurzweil integrable then \(x\in[0,1]\) is a point of \textit{non-summability} (`\textit{singular point}' in the paper under review) if \(\int_I|f|\) diverges for every open interval \(x\in I\subset[0,1]\). An example shows that for each \(0<\lambda<1\) there is a Henstock--Kurzweil integrable function \(f\) such that the set of points of non-summability has measure \(\lambda\). All the results of this paper, including the definition of point of non-summability and the example, are contained in pages 147-149 of [\textit{R. L. Jeffery}, ``The theory of functions of a real variable'' (1951; Zbl 0043.27901)].
reviewed by: Erik Talvila
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 1848802
zbMATH Keywords: singular point
zbMATH Keywords: Henstock-Kurzweil integrable function
zbMATH Keywords: point of non-summability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1848802