On the points of regularity of multivariate functions of bounded variation
type: Item
instance of: scholarly article
title: On the points of regularity of multivariate functions of bounded variation
zbMATH Open document ID: 1064.26007
author: Burkhard Lenze
published in: Real Analysis Exchange
publication date: 2005-04-04T00:00:00Z
review text: Points of non-regularity are studied for multivariate functions of bounded variation, denoted BV. Among numerous versions of the latter notion the author chooses to deal with that connected with the names of Vitali, Lebesgue, Fréchet, and de la Vallée Poussin which proved to be useful in the theory of measure and integration but less in the theory of trigonometric series, where the Hardy variation is more suitable. It is shown in the paper that BV functions vanishing at infinity are non-regular at most on a subset of \(\mathbb R^n\) Lebesgue measure zero, and the result is best possible.
reviewed by: Elijah Liflyand
Mathematics Subject Classification ID: 26B30
zbMATH DE Number: 2151933
zbMATH Keywords: bounded variation
zbMATH Keywords: multivariate function
zbMATH Keywords: points of regularity
MaRDI profile type: Publication
full work available at URL: realanalexch.29.2.0647
OpenAlex ID: W1588168685
DOI: 10.14321/REALANALEXCH.29.2.0647
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description: scientific article; zbMATH DE number 2151933