A pair of adjoint classes of Riemann-Stieltjes integrable functions
type: Item
instance of: scholarly article
title: A pair of adjoint classes of Riemann-Stieltjes integrable functions
zbMATH Open document ID: 0944.26017
author: Hanxiang Chen
published in: Real Analysis Exchange
publication date: 2000-05-21T00:00:00Z
review text: Let \(-\infty <a<b<\infty \) and let R stand for the set of functions Riemann integrable on \([a,b].\) The author shows that then the Riemann-Stieltjes integral \(\int _a^b f dg\) exists for all \(f\in \text R\) and any function \(g\) absolutely continuous on \([a,b]\) (\(g\in \) AC). Moreover, if \(\int _a^b f dg\) exists for all \(f\in \) R, then \(g\in \) AC and if \(\int _a^b f dg\) exists for all \(g\in \) AC, then \(f\in \) R. (In other words, the sets R and AC are adjoint with respect to the Riemann-Stieltjes integral).
Mathematics Subject Classification ID: 26A42
Mathematics Subject Classification ID: 26A46
Mathematics Subject Classification ID: 26A45
zbMATH DE Number: 1449414
zbMATH Keywords: adjoint classes
zbMATH Keywords: Riemann integrable function
zbMATH Keywords: Riemann-Stieltjes integral
zbMATH Keywords: functions of bounded variation
zbMATH Keywords: absolutely continuous functions
reviewed by: Milan Tvrdý
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1449414