| Résume | The group Sym(Ω) of all permutations of a countably infinite set Ω admits natural probability measure-preserving (p.m.p.) actions on product probability spaces (A, κ)^Ω, known as Bernoulli shifts. In an ongoing joint work with Colin Jahel and Emmanuel Roy, we describe the factors (that is, the invariant sub-σ-algebras) of such Bernoulli shifts. Our description applies not only to Sym(Ω), but also to any subgroup of Sym(Ω) that satisfies a version of de Finetti’s theorem. |
