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arXiv · 1405.2527

Countable tightness in the spaces of regular probability measures

Grzegorz Plebanek·Damian Sobota
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Abstract

We prove that if $K$ is a compact space and the space $P(K\times K)$ of regular probability measures on $K\times K$ has countable tightness in its $weak^*$ topology, then $L_1(μ)$ is separable for every $μ\in P(K)$. It has been known that such a result is a consequence of Martin's axiom MA$(ω_1)$. Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todorčević on measures on Rosenthal compacta.

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Grzegorz Plebanek, Damian Sobota. 2014-05-11. Countable tightness in the spaces of regular probability measures. https://arxiv.org/abs/1405.2527

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