Reznichenko E. A. Stone-cech extensions of probability measure spaces // ArXiv e-prints. — 2025. — P. 1–30.
Аннотация
It is proved that P(βX)=βP(X) if and only if P(X) is a pseudocompact space, where P(X) is the space of probability Radon measures with weak topology and βX is a Stone-Cech extension of the space 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.