Amenability, hyperfiniteness, and isoperimetric inequalities

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• 作者：Kaimanovich ; Vadim A.
• 刊名：Comptes Rendus de l'Academie des Sciences Series I Mathematics
• 出版年：1997
• 期刊代码：10_07644442
• 类别：mt
• 出版时间：November, 1997
• 卷：325
• 期：9
• 页码：999-1004
• 文件大小：366 K

摘要

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.