Japan. J. Math. 19, 143--180 (2024)

A survey on topological properties of $P(K)$ spaces

Grzegorz Plebanek

Abstract: Given a compact space $K$, we denote by $P(K)$ the space of all Radon probability measures on $K$, equipped with the $weak^\ast$ topology inherited from $C(K)^\ast$. For nonmetrizable compacta $K$ even basic properties of $P(K)$ spaces depend of additional axioms of set theory. We discuss here older and quite recent results on the subject.