Definable convolution and idempotent Keisler measures
Logic
2021-01-19 v3
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.
Keywords
Cite
@article{arxiv.2004.10378,
title = {Definable convolution and idempotent Keisler measures},
author = {Artem Chernikov and Kyle Gannon},
journal= {arXiv preprint arXiv:2004.10378},
year = {2021}
}
Comments
v3. 30 pages; minor corrections and clarifications throughout the article; accepted to the Israel Journal of Mathematics