On the existence of the Stieltjes integral
type: Item
instance of: scholarly article
title: On the existence of the Stieltjes integral
zbMATH Open document ID: 0910.26004
author: A. M. D'yachkov
published in: Doklady Mathematics
publication date: 1998-06-23T00:00:00Z
review text: The paper includes several theorems concerning the existence of the Hellinger integral. As corollaries, the author has obtained results about the Stieltjes integral. A typical example is Theorem 2: For a function \(f\) which is Riemann integrable the following conditions are equivalent: 1) the Hellinger integral \(I_H(f,g)\) exists for all \(g\) of bounded \(\Phi\)-variation, 2) the Hellinger integral \(I_H(f, g)\) exists for all \(\Phi\)-continuous \(g\).
Mathematics Subject Classification ID: 26A42
zbMATH DE Number: 1148055
zbMATH Keywords: Hellinger integral
zbMATH Keywords: Stieltjes integral
reviewed by: Jerzy Niewiarowski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1148055