Countable tightness in the spaces of regular probability measures

Grzegorz Plebanek, and Damian Sobota. "Countable tightness in the spaces of regular probability measures." Fundamenta Mathematicae 229.2 (2015): 159-169. <http://eudml.org/doc/282805>.

@article{GrzegorzPlebanek2015,
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.},
author = {Grzegorz Plebanek, Damian Sobota},
journal = {Fundamenta Mathematicae},
keywords = {tightness of topological spaces; countable tightness of measures; Maharam type},
language = {eng},
number = {2},
pages = {159-169},
title = {Countable tightness in the spaces of regular probability measures},
url = {http://eudml.org/doc/282805},
volume = {229},
year = {2015},
}

TY - JOUR
AU - Grzegorz Plebanek
AU - Damian Sobota
TI - Countable tightness in the spaces of regular probability measures
JO - Fundamenta Mathematicae
PY - 2015
VL - 229
IS - 2
SP - 159
EP - 169
AB - 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.
LA - eng
KW - tightness of topological spaces; countable tightness of measures; Maharam type
UR - http://eudml.org/doc/282805
ER -