Monolithic spaces of measures

Grzegorz Plebanek

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arXiv · 1912.13297

Monolithic spaces of measures

Grzegorz Plebanek

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Abstract

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.

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BibTeX RIS

Grzegorz Plebanek. 2020-09-17. Monolithic spaces of measures. https://arxiv.org/abs/1912.13297

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