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Preprint Number 835
835. Artem Chernikov and Pierre Simon
Definably amenable NIP groups
Submission date: 15 February 2015.
We study definably amenable NIP groups. We develop a theory of generics, showing that various definitions considered previously coincide, and study invariant measures. Applications include: characterization of regular ergodic measures, a proof of the conjecture of Petrykowski connecting existence of bounded orbits with definable amenability in the NIP case, and the Ellis group conjecture of Newelski and Pillay connecting the model-theoretic connected component of an NIP group with the ideal subgroup of its Ellis enveloping semigroup.
Mathematics Subject Classification: 03C45, 37B05, 03C60, 03C64, 22F10, 28D15
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