Amenability, Hyperrniteness and Isoperimetric Inequalities

  title={Amenability, Hyperrniteness and Isoperimetric Inequalities},
  author={Vadim A. Kaimanovich},
We formulate two new criteria of amenability of discrete equivalence relations: in terms of asymptotically invariant families of leafwise probability measures and in terms of isoperimetric properties of leafwise graph structures. These criteria lead to a geometric proof of the Connes{Feldman{Weiss theorem on coincidence of amenability and hyperrniteness for equivalence relations. Nous consid erons les relations d' equivalence discr etes R sur les espaces mesurables de Lebesgue (X;). Les… CONTINUE READING