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

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.