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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-2-4,
author = {Grzegorz Plebanek and Damian Sobota},
title = {Countable tightness in the spaces of regular probability measures},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {159-169},
zbl = {1333.46024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-2-4}
}
Grzegorz Plebanek; Damian Sobota. Countable tightness in the spaces of regular probability measures. Fundamenta Mathematicae, Tome 228 (2015) pp. 159-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-2-4/