Geodesic
Countable tightness in the spaces of regular probability measures
Grzegorz Plebanek1 ; Damian Sobota2
1Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland
Fundamenta Mathematicae, Tome 229 (2015) no. 2, pp. 159-169
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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 $L_1(\mu )$ is separable for every $\mu \in P(K)$. It has been known that such a result is a consequence of Martin's axiom MA$(\omega _1)$. Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todorčević on measures on Rosenthal compacta.
DOI : 10.4064/fm229-2-4
Keywords: prove compact space space times regular probability measures times has countable tightness its weak * topology separable every has known result consequence martins axiom omega theorem has several consequences particular generalizes theorem due bourgain todor evi measures rosenthal compacta

Grzegorz Plebanek  1   ; Damian Sobota  2

1 Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland 
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Grzegorz Plebanek; Damian Sobota. Countable tightness in the spaces of
 regular probability measures. Fundamenta Mathematicae, Tome 229 (2015) no. 2, pp. 159-169. doi: 10.4064/fm229-2-4

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