Some comments on an approximately continuous Khintchine integral
type: Item
instance of: scholarly article
title: Some comments on an approximately continuous Khintchine integral
zbMATH Open document ID: 0847.26011
author: Russell A. Gordon
published in: Real Analysis Exchange
publication date: 1996-10-06T00:00:00Z
review text: The author defines the \(AK_N\) integral and shows that it includes the general Denjoy (Khintchine) integral, the approximately continuous integral of Burkill, and the Kubota integral. A function \(f\) is \(AK_N\) integrable on \([a, b]\) if there is an approximately continuous function \(F\) which is BVG and satisfies Lusin's condition such that the approximate derivative \(F_{ap}'= f\) almost everywhere in \([a, b]\). For a Riemann-type definition of the Kubota integral, see \textit{T.-Y. Lee} and \textit{P.-Y. Lee} [Math. Jap. 42, No. 2, 257-263 (1995; Zbl 0844.26006)].
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 801041
zbMATH Keywords: Denjoy integral
zbMATH Keywords: Khintchine integral
zbMATH Keywords: approximately continuous integral of Burkill
zbMATH Keywords: Kubota integral
reviewed by: Peng-Yee Lee
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 801041