Logic Seminar

Given a countable Borel equivalence relation on a standard Borel space X, when do two measures agree on the invariant sets? By a result of Þórisson, if G is a countable group generating the equivalence relation, then this property holds iff there exists a measure on G\times X whose pushforwards under the projection and the action are the original measures. We will investigate this and other equivalent formulations of this property.