Extensions of discrete and equal Baire functions
type: Item
instance of: scholarly article
title: Extensions of discrete and equal Baire functions
zbMATH Open document ID: 0731.54015
DOI: 10.1007/BF01903710
published in: Acta Mathematica Hungarica
publication date: 1990-01-01T00:00:00Z
review text: In the paper by the author and \textit{M. Laczkovich} [Studia Sci. Math. Hungar. 10, 463-472 (1975; Zbl 0405.26006)] discrete and equal convergence of sequences of real-valued functions have been introduced. Namely, we say that f is the discrete limit of \(\{f_ n\}\), if for every \(x\in X\) there exists \(n_ 0=n_ 0(x)\) such that \(f(x)=f_ n(x)\) for \(n\geq n_ 0\). Further, f is said to be the equal limit of the sequence \(\{f_ n\}\) if there is a sequence of positive numbers \(\epsilon_ n\to 0\) such that, for every \(x\in X\) there exists \(n_ 0=n(x)\) with \(| f(x)-f_ n(x)| <\epsilon_ n\), for \(n\geq n_ 0\). Subsequently, in two follow-up articles (ibid.) corresponding Baire classes of functions have been studied. In this note, extensions of the mentioned classes of functions are investigated.
Mathematics Subject Classification ID: 54C50
Mathematics Subject Classification ID: 54C20
zbMATH DE Number: 4209058
zbMATH Keywords: discrete convergence
zbMATH Keywords: equal convergence
zbMATH Keywords: discrete limit
zbMATH Keywords: equal limit
zbMATH Keywords: Baire classes of functions
author: Ákos Császár
reviewed by: Zbigniew Piotrowski
MaRDI profile type: Publication
cites work: Q4190850
cites work: Some remarks on discrete Baire classes
cites work: Q5541833
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description: scientific article; zbMATH DE number 4209058