This is an announcement for the paper "Countable tightness in the spaces of regular probability measures" by Grzegorz Plebanek and Damian Sobota. 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 $L_1(\mu)$ 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 Todor\v{c}evi\'c on measures on Rosenthal compacta. Archive classification: math.FA Mathematics Subject Classification: Primary 46E15, 46E27, 54C35 Remarks: 9 pages Submitted from: grzes@math.uni.wroc.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.2527 or http://arXiv.org/abs/1405.2527