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Slawomir Solecki - Polish group actions and measures

SLAWOMIR SOLECKI, Indiana University
Polish group actions and measures

The talk will be about a connection between continuous actions of Polish groups and the structure of the equivalence relation of mutual absolute continuity among Borel probability measures defined on a Polish space. We will show that this equivalence relation is induced by a special kind of a continuous action of a Polish group. Background and consequences of this result will be presented. For example, a theorem of Kechris and Sofronidis (that it is not possible to classify, by ``simple objects'' and in Baire measurable fashion, Borel probability measures up to mutual absolute continuity) will be deduced.


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