Countable tightness in the spaces of regular probability measures

摘要

We prove that if K is a compact space and the space P(K x K) of regular probability measures on K x K has countable tightness in its weak* topology, then L-1(mu) is separable for every mu is an element of 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 Todorcevic on measures on Rosenthal compacta.