The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

Abstract

We prove that a homogeneous space G/H, with G a locally compact group and H a closed subgroup of G, is amenable in the sense of Eymard–Greenleaf if and only if the quasiregular action π_Φ of G on the unit sphere of the Orlicz space L^Φ(G/H) for some N-function Φ ∈ Δ₂ satisfies the Rao–Reiter condition (P_Φ).