On a generalization of Egoroff's theorem
type: Item
instance of: scholarly article
zbMATH Open document ID: 0979.28001
author: Shozo Niizeki
publication date: 2001-08-14T00:00:00Z
Mathematics Subject Classification ID: 28A20
zbMATH DE Number: 1605050
zbMATH Keywords: Egoroff's theorem
zbMATH Keywords: uniform convergence
MaRDI profile type: Publication
title: On a generalization of Egoroff's theorem
published in: Memoirs of the Faculty of Science. Series A. Mathematics
review text: Standard techniques are used to prove a slight variation of Egoroff's theorem, namely that if a sequence \(\{f_n\}\) of measurable real valued functions converges on a set \(A\), then the sequence converges almost uniformly on any subset \(B \subseteq A\) of finite measure. A standard example showing the need for finiteness of the measure of \(B\) is presented as well.
reviewed by: J. W. Hagood
description: scientific article; zbMATH DE number 1605050