  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.
