Definable convolution and idempotent Keisler measures

2020/04/22 by Artem Chernikov, Kyle Gannon, Chernikov, Artem +1 · 2 citations
Computer Science · Mathematics · #03C45 #03C60 #28D15 #37B05 #43A10 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2004.10378

openalex publication_date 2020/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We initiate a systematic study of the convolution operation on Keisler measures, generalizing the work of Newelski in the case of types. Adapting results of Glicksberg, we show that the supports of generically stable (or just definable, assuming NIP) measures are nice semigroups, and classify idempotent measures in stable groups as invariant measures on type-definable subgroups. We establish left-continuity of the convolution map in NIP theories, and use it to show that the convolution semigroup on finitely satisfiable measures is isomorphic to a particular Ellis semigroup in this context.

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