Amenability and Ramsey theory in the metric setting

Abstract

Moore characterized the amenability of automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to automorphism groups of metric Fraïssé structures, which encompass all Polish groups. As an application, we prove that amenability is a G_delta condition.

References in corpus (2)

• Generic representations of abelian groups and extreme amenability
• Extremely amenable groups via continuous logic