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Finite graphs and amenability

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/11/2012
<mark>Journal</mark>Journal of Functional Analysis
Issue number9
Volume263
Number of pages22
Pages (from-to)2593-2614
Publication statusPublished
Original languageEnglish

Abstract

Hyperfiniteness or amenability of measurable equivalence relations and group actions has been studied for almost fifty years. Recently, unexpected applications of hyperfiniteness were found in computer science in the context of testability of graph properties. In this paper we propose a unified approach to hyperfiniteness. We establish some new results and give new proofs of theorems of Schramm, Lovász, Newman–Sohler and Ornstein–Weiss.