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Wednesday, November 13, 2019

**Abstract:** Given a countable Borel equivalence relation $E$ on a standard Borel space, we give a construction of a hyperfinite subequivalence relation $F \subseteq E$ such that every $E$-invariant $E$-ergodic probability measure $\nu$ is also $F$-ergodic. The construction also yields the uniform ergodic decomposition theorem for $E$.