POSITIVITY, cilt.23, sa.3, ss.507-521, 2019 (SCI-Expanded)
In this paper we investigate the distance of convergence in measure whenever the measure is not sigma-finite and identify the topological coreflection of this approach structure with a direct proof. Also we investigate its connections with metric approach structures on spaces of measurable functions and obtain some results for integrability of measurable functions in this setting.