Logic Seminar

Let Gamma be a countable group. The invariant random subgroup of a pmp action of Gamma on X is the measure on the space of subgroups of Gamma obtained by pushing forward the measure on X via the map sending x to its stabilizer. A result of Elek states that if two pmp actions of Gamma have the same invariant random subgroup and one is hyperfinite, then they are strongly equivalent, so in particular they are both hyperfinite. We present a proof due to Giraud.