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Wednesday, November 6, 2019

**Abstract:** An equivalence relation on a standard Borel space is called *hyperfinite* if it is a countable increasing union of Borel equivalence relations whose classes are finite. We will prove the natural pointwise ergodic theorem for probability measure preserving hyperfinite equivalence relations, as recorded by Miller and Tserunyan in [MTs17]. If time permits, Anush Tserunyan will continue with a prelude to the next talk on proving the existence of a uniformly ergodic hyperfinite subequivalence relation of a given pmp countable Borel equivalence relation.