Sur les espaces test pour la moyennabilit\'e

摘要: We observe that a Polish group $G$ is amenable if and only every continuous action of on the Hilbert cube admits an invariant probability measure. This generalizes result Bogatyi Fedorchuk. also show actions Cantor space can be used to detect amenability extreme non-archimedean groups as well at infinity discrete countable groups. As corollary, latter property tested by cube. These results generalize criterion due Giordano de la Harpe.