Mappings and Prohorov spaces

AbstractWe consider completely regular Hausdorff spaces. In this paper we investigate the space of probability Radon measures P(X) on a space X and the property to be a Prohorov space. We prove that the space P(X) is sieve-complete if and only if X is sieve-complete. Every mapping φ:X→Y generates the mapping P(φ):P(X)→P(Y). Some properties of the mapping P(φ) are studied. In particular, we investigate under which conditions the open continuous image of a Prohorov space is Prohorov