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Finding generically stable measures

  • Pierre Simon (a1)

This work builds on previous papers by Hrushovski, Pillay and the author where Keisler measures over NIP theories are studied. We discuss two constructions for obtaining generically stable measures in this context. First, we show how to symmetrize an arbitrary invariant measure to obtain a generically stable one from it. Next, we show that suitable sigma-additive probability measures give rise to generically stable Keisler measures. Also included is a proof that generically stable measures over o-minimal theories and the p-adics are smooth.

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[2] Ehud Hrushovski , Ya'acov Peterzil , and Anand Pillay , Groups, measures, and the NIP, Journal of the American Mathematical Society, vol. 21 (2008), no. 2, pp. 563596.

[4] H. Jerome Keisler , Measures and forking, Annals of Pure and Applied Logic, vol. 34 (1987), no. 2, pp. 119169.

[7] Itaï Ben Yaacov , Continuous and random vapnik-chervonenkis classes, Israel Journal of Mathematics, vol. 173 (2009), pp. 309333.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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