Difference functions for functions with the Baire property
type: Item
instance of: scholarly article
title: Difference functions for functions with the Baire property
zbMATH Open document ID: 0988.54031
author: M. Balcerzak
author: Elżbieta Kotlicka
author: Wojciech Wojdowski
published in: Aequationes Mathematicae
publication date: 2002-07-09T00:00:00Z
review text: Let \(G\) be the additive group \(\mathbb R\) or \(\mathbb R/\mathbb Z\). For \(f:G\to\mathbb R\) and \(h\in G\) the difference function is defined by \(\Delta_hf(x)=f(x+h)-f(x)\). For families \(\mathcal G\subset\mathcal F\) of functions \(f:G\to\mathbb R\) let \(\mathcal H(\mathcal F,\mathcal G)= \{H\subset G:\exists f\in\mathcal F\smallsetminus\mathcal G\) \(\forall h\in H\) \(\Delta_hf\in\mathcal G\}\). \textit{T. Keleti} in his thesis studied such families for several families \(\mathcal F\), \(\mathcal G\) of measurable functions. In the paper under the review the authors prove analogous results for families of functions with the Baire property. In particular, for \(\mathcal G\) the family of functions with the Baire property is considered and for \(\mathcal F\) two of its subfamilies, the family of functions which are almost everywhere equal to a continuous function and the family of functions which are almost everywhere equal to a bounded function (``almost everywhere'' here means with respect to the first category).
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 54E52
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 26A99
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 1320502
zbMATH Keywords: difference function
zbMATH Keywords: additive function
zbMATH Keywords: Baire property
MaRDI profile type: Publication
full work available at URL: s000100050083
OpenAlex ID: W2027195923
DOI: 10.1007/S000100050083
description: scientific article; zbMATH DE number 1320502