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Monolithic spaces of measures

Volume 254 / 2021

Grzegorz Plebanek Fundamenta Mathematicae 254 (2021), 335-348 MSC: Primary 28A33, 46E27, 03E50. DOI: 10.4064/fm962-9-2020 Published online: 14 January 2021

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.

Authors

  • Grzegorz PlebanekInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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