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In [M2], Moore characterizes 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 δ condition.doi:10.4064/fm231-1-2 fatcat:jv7sslxrpzebpahqp7zr6legqe