Abstract and Applied Analysis
Volume 2011 (2011), Article ID 582576, 7 pages
http://dx.doi.org/10.1155/2011/582576
Research Article

On 𝑝 -Convergence in Measure of a Sequence of Measurable Functions

A. Boccuto,1 Ch. Papachristodoulos,2 and N. Papanastassiou2

1Department of Mathematics and Computer Sciences, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
2Department of Mathematics, University of Athens, Panepistimiopolis, 15784 Athens, Greece

Received 18 November 2010; Accepted 22 March 2011

Academic Editor: Agacik Zafer

Copyright © 2011 A. Boccuto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the study by Papanastassiou and Papachristodoulos, 2009 the notion of 𝑝 -convergence in measure was introduced. In a natural way 𝑝 -convergence in measure induces an equivalence relation on the space 𝑀 of all sequences of measurable functions converging in measure to zero. We show that the quotient space ℳ is a complete but not compact metric space.