Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Applied Analysis

Editor-in-Chief: Fechner, Włodzimierz / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

CiteScore 2018: 0.45

SCImago Journal Rank (SJR) 2018: 0.181
Source Normalized Impact per Paper (SNIP) 2018: 0.845

Mathematical Citation Quotient (MCQ) 2018: 0.20

See all formats and pricing
More options …
Volume 18, Issue 2


On the Lebesgue density theorem

Władysław Wilczyński
Published Online: 2012-11-27 | DOI: https://doi.org/10.1515/jaa-2012-0018


The classical Lebesgue density theorem says that almost each point of a measurable set A is a density point of A. It is well known that the density point of a measurable set A can be described in terms of the convergence in measure of a sequence of characteristic functions of sets similar to A. In this note it is shown that in the Lebesgue density theorem the convergence in measure cannot be replaced by the convergence almost everywhere.

Keywords: Density point; Lebesgue density theorem; convergence almost everywhere and in measure

About the article

Received: 2011-10-21

Revised: 2012-01-31

Accepted: 2012-02-09

Published Online: 2012-11-27

Published in Print: 2012-12-01

Citation Information: , Volume 18, Issue 2, Pages 275–281, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/jaa-2012-0018.

Export Citation

© 2012 by Walter de Gruyter Berlin Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in