In the study by Papanastassiou and Papachristodoulos, 2009 the notion of -convergence in measure was introduced. In a natural way -convergence in measure induces an equivalence relation on the space of all sequences of measurable functions converging in measure to zero. We show that the quotient space is a complete but not compact metric space.
A. Boccuto. Ch. Papachristodoulos. N. Papanastassiou. "On -Convergence in Measure of a Sequence of Measurable Functions." Abstr. Appl. Anal. 2011 1 - 7, 2011. https://doi.org/10.1155/2011/582576