Spaces of Measures as Mackey Completions

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‘; 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‘