Monolithic spaces of measures
Volume 254 / 2021
Fundamenta Mathematicae 254 (2021), 335-348 MSC: Primary 28A33, 46E27, 03E50. DOI: 10.4064/fm962-9-2020 Published online: 14 January 2021
For a compact space $K$ we consider the space $P(K)$ of probability regular Borel measures on $K$, equipped with the weak$^\ast $ topology inherited from $C(K)^\ast $. We discuss possible characterizations of those compact spaces $K$ for which $P(K)$ is $\aleph_0$-monolithic. The main result states that under $\diamondsuit $ there exists a nonseparable Corson compact space $K$ such that $P(K)$ is $\aleph_0$-monolithic but $K$ supports a measure of uncountable type.