Gromov’s measure equivalence and rigidity of higher rank lattices

  title={Gromov’s measure equivalence and rigidity of higher rank lattices},
  author={Alex Furman},
  journal={Annals of Mathematics},
  • A. Furman
  • Published 1 November 1999
  • Mathematics
  • Annals of Mathematics
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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