Medidas perfectas y teorema de representación

Abstract

Diverse topologies have been studied on the Cb(X,E) space, of the continuous and bounded functions from X into E, with X completely regular Hausdorff space and E a normed space, for the purpose of identifying their dual with some measure’ space. In this article the perfect topology is described, being defined over Cb(X,E) and induced by distinguished sets, such as the perfect measure’ space from Ba*(X) into E’, where Ba*(X) denotes the algebra of Baire generated by the zero sets of X and E’ is the dual space of (E, ǁ.ǁ). The dual underlying relation is used for the representation of a linear continuous operator defined from the space (Cb (X,E) ; p) to a Banach space.