qm-Sequence characterizations of certain measure-theoretic and topological properties

Abstract

In this thesis we shall study some relations between the concepts of Measure and Topology. The spaces which are considered are assumed to be at least Tychonoff, that is a T1 space X on which every point x and every closed set F disjoint from x are functionally seperated. Let us denote by M(X), Mo(X), MT(X) and Mt(X) the sets of all regular measures, o-additive measures, t-additive measures and tight measures on a Tychnonoff space X respectively, and by T(X), To(X), Tt(X) and D(X) the sets of all two-valued measures, two-valued o-additive measures, two-values T-additive measures and Dirac measures on a Tychonoff space X respectively.