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Finding generically stable measures

Published online by Cambridge University Press:  12 March 2014

Pierre Simon
Pierre Simon*
Affiliation:
ENS, Département de Mathématiques et Applications, 45, Rue D'ulm, 75005 Paris, France, E-mail: pierre.simon.05@normalesup.org
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 1 , March 2012 , pp. 263 - 278
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

[1]Hrushovsk, Ehud, Pillay, Anand, and Simon, Pierre, Generically stable and smooth measures in NIP theories, Submitted.Google Scholar
[2]Hrushovski, Ehud, Peterzil, Ya'acov, and Pillay, Anand, Groups, measures, and the NIP, Journal of the American Mathematical Society, vol. 21 (2008), no. 2, pp. 563–596.CrossRefGoogle Scholar
[3]Hrushovski, Ehud and Pillay, Anand, On nip and invariant measures, Journal of the European Mathematical Society, vol. 13 (2011), pp. 1005–1061.Google Scholar
[4]Keisler, H. Jerome, Measures and forking, Annals of Pure and Applied Logic, vol. 34 (1987), no. 2, pp. 119–169.CrossRefGoogle Scholar
[5]Shelah, Saharon, Classification theory for elementary classes with the dependence property—a modest beginning, Scientiae Mathematicae Japonicae, vol. 59 (2004), no. 2, pp. 265–316, Special issue on set theory and algebraic model theory.Google Scholar
[6]Simon, Pierre, Distal and non-distal theories, 2011.Google Scholar
[7]Yaacov, Itaï Ben, Continuous and random vapnik-chervonenkis classes, Israel Journal of Mathematics, vol. 173 (2009), pp. 309–333.CrossRefGoogle Scholar
[8]Yaacov, Itaï Ben, Transfer of properties between measures and random types, in preparation, 2009.Google Scholar