Resolvability of Measurable Spaces

Abstract

We consider a special kind of structure resolvability and irresolvability for measurable spaces and discuss analogues of the criteria for topological resolvability and irresolvability.

Density, Smital Property and Quasicontinuity

“…The notion of density is strictly connected with the resolvability of a topological space and also, in a more general setting, with the resolvability of a measurable space (X, A, I) [4] and with structure resolvability [6]. If F is a family of nonempty subsets of X, we say that the family (X, F ) is α-resolvable if there exists a family of cardinality α of pairwise disjoint sets which are dense with respect to F .…”

“…It is easily seen that no topology is needed to formulate and study the Smital property. It is enough to define a family of dense sets, as in [6] and [4].…”