Countable tightness in the spaces of regular probability measures

2014/05/11 by Grzegorz Plebanek, Plebanek, Grzegorz, Damian Sobota +1
Mathematics · #46E27 #54C35 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46E15 #math.FA #msc:46E15 #msc:46E27 #msc:54C35

paper · pdf · doi:10.48550/arxiv.1405.2527

9 pages

arxiv created 2014/05/11 · arxiv updated 2014/05/13

Abstract

We prove that if K is a compact space and the space P(K× K) of regular probability measures on K× K has countable tightness in its weak^* topology, then L₁(μ) is separable for every μ∈ P(K). It has been known that such a result is a consequence of Martin's axiom MA(ω₁). 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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