713 research outputs found
Finite graphs and amenability
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
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