On the density topology with respect to an extension of Lebesgue measure
type: Item
instance of: scholarly article
title: On the density topology with respect to an extension of Lebesgue measure
zbMATH Open document ID: 0879.28004
published in: Real Analysis Exchange
publication date: 1997-12-10T00:00:00Z
review text: The author studies the density topology generated by complete extensions of Lebesgue measure. He proves that for any complete extension \(\mu\) of Lebesgue measure the corresponding \(\mu\)-density topology is the Hashimoto topology of the form \(\tau^*_\mu =\{X\subset \mathbb R: X=Y\setminus Z,\^^MY\in \tau_d,\;\mu (Z)=0\}\), where \(\tau_d\) is the density topology derived from the Lebesgue measure. As a consequence of the theorems proved in the article the author obtained the following: For any complete extension \(\mu\) of Lebesgue measure, the family of the real functions continuous in the \(\mu\)-density topology coincides with the family of all approximately continuous functions.
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 1095879
zbMATH Keywords: extension of Lebesgue measure
zbMATH Keywords: density point
author: Jacek Hejduk
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1095879