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Preprint Number 2140

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2140. Artem Chernikov and Kyle Gannon
Definable convolution and idempotent Keisler measures II

Submission date: 26 February 2122


We study convolution semigroups of invariant/finitely satisfiable Keisler measures in NIP groups. We show that the ideal (Ellis) subgroups are always trivial and describe minimal left ideals in the definably amenable case, demonstrating that they always form a Bauer simplex. Under some assumptions, we give an explicit construction of a minimal left ideal in the semigroup of measures from a minimal left ideal in the corresponding semigroup of types (this includes the case of SL_{2}(ℝ), which is not definably amenable). We also show that the canonical push-forward map is a homomorphism from definable convolution on G to classical convolution on the compact group G/G^{00}, and use it to classify G^{00}-invariant idempotent measures.

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

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Full text arXiv 2202.13232: pdf, ps.

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