Stone-Cech Compactifications of Spaces of Probability Measures

Abstract

It is proved that $P(\beta X)=\beta P(X)$ if and only if $P(X)$ is a pseudocompact space, where $P(X)$ is the space of Radon probability measures with the weak topology and $\beta X$ is the Stone--\v Cech compactification of $X$. A locally compact pseudocompact space $X$ is constructed such that $P(X)$ is not pseudocompact. Conditions are obtained under which $P(X)$ is pseudocompact.