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( ) is separable for every 2 P(K). It has been known that such a result is a consequence of Martin's axiom MA(!1). Our theorem has several consequences; in particular, it general- izes a theorem due to Bourgain and Todor£evi¢ on measures on Rosenthal compacta. 1. Introduction. The tightness of a topological space X, denoted by (X), is the least cardinal number such that for every A X and x2 A there is a set A0 A withjA0j (X) and such that x2 A0. Throughout, K stands for a compact Hausdor topological space. By
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