On “essentially metrizable” spaces and on measurable functions with values in such spaces

Introduction. In this paper we consider uniform spaces in which also a measure ,u is defined and which possess certain topological properties either to the full extent or only "essentially" ("ess."), i.e. to within sets of measure zero, in a sense to be defined below. We shall define such notions as "ess. metrizability", "ess. separability", etc. Conditions for the ess. metrizability of a uniform space T