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Gromov's measure equivalence and rigidity of higher rank lattices

Alex Furman
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Abstract

In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the motivations for this notion. The main result of this paper is ME rigidity of higher rank lattices: any countable group which is ME to a lattice in a simple Lie group G of higher rank, is commensurable to a lattice in G.

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Alex Furman. 1999-11-01. Gromov's measure equivalence and rigidity of higher rank lattices. https://arxiv.org/abs/math/9911262

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