Amenability and Ramsey theory in the metric setting
classification
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math.DS
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amenabilitygroupsautomorphismmetricstructuresapplicationcharacterizedcondition
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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 Fra\"iss\'e structures, which encompass all Polish groups. As an application, we prove that amenability is a G_delta condition.
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