Weak compactness of vector measures on topological spaces

Abstract

Let X be a completely regular Hausdorff space, E a quasi-complete locally convex space, C b (X) the space of all bounded, scalar-valued continuous functions on X, and B(X) and B 0 (X) be the classes of Borel and Baire subsets of X.We study the subsets of the spaces M t (X, E), M τ (X, E), M σ (X, E) of respectively tight, τ -smooth, and σ-smooth, E-valued measures on X for weak compactness.