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Preprint Number 1767

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1767. Artem Chernikov and Kyle Gannon
Definable convolution and idempotent Keisler measures
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Submission date: 22 April 2020

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.

Mathematics Subject Classification: 03C45, 37B05, 43A10, 03C60, 28D15

Keywords and phrases:

Full text arXiv 2004.10378: pdf, ps.


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