Mappings and Prohorov spaces (Q2499788)

A space \(X\) is called a Prohorov space if every compact subset of probability Radon measures \(P(X)\) on \(X\) is uniformly tight. In this paper the author investigates the space \(P(X)\) and the property of being a Prohorov space. It is proved that the space \(P(X)\) is sieve-complete iff \(X\) is sieve-complete. Each mapping \(\varphi :X\rightarrow Y\) generates the mapping \(P(\varphi ):P(X) \rightarrow P(Y)\). The author studies various properties of \(P(\varphi )\). In particular: under which conditions the open continuous image of a Prohorov space is a Prohorov space.