Amenability and Ramsey theory in the metric setting

摘要

Moore [Fund. Math. 220 (2013)] characterizes the amenability of the automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to the automorphism groups of metric Fraisse structures, which encompass all Polish groups. As an application, we prove that amenability is a G(delta) condition.