Gabor Elek
Published 2012-04-02, updated 2012-05-30Version 2
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, Lov\'asz, Newman-Sohler and Ornstein-Weiss.
On amenability and groups of measurable maps
Amenability and harmonic $L^p$-functions on hypergroups
Amenability of ultraproducts of Banach algebras
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