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Gromov’s measure equivalence and rigidity of higher rank lattices. (English) Zbl 0943.22013

Author’s 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 \(G\)”.
Reviewer: S.K.Kaul (Regina)

MSC:

22E40 Discrete subgroups of Lie groups
37A05 Dynamical aspects of measure-preserving transformations
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