Spaces of Measures as Mackey Completions

Abstract

Let X be a completely regular Hausdorff space, let E be a normed space, let C X E C X if E is scalars) be the space of all E-valued continuous functions on X, and let L X be the vector space of discrete measures on X. There is a natural duality between L X and C X . In this paper the completion of the space L X τ L X C X is investigated and considering the elements as measures, many properties are proved. Several results are also extended to C X E