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

Abstract

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