论文信息 - Amenability, hyperfiniteness, and isoperimetric inequalities

Amenability, hyperfiniteness, and isoperimetric inequalities

Abstract We formulate two new criteria of amenability of discrete equivalence relations: in terms of asymptotically invariant families of leafwise probability measures and in terms of isoperimetric properties of leafwise graph structures. These criteria lead to a geometric proof of the Connes-Feldman-Weiss theorem on coincidence of amenability and hyperfiniteness for equivalence relations.

Vadim A. Kaimanovich | V. Kaimanovich

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