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Generically stable and smooth measures in NIP theories


Authors: Ehud Hrushovski, Anand Pillay and Pierre Simon
Journal: Trans. Amer. Math. Soc. 365 (2013), 2341-2366
MSC (2010): Primary 03C68, 03C45, 22C05, 28E05
Published electronically: December 13, 2012
MathSciNet review: 3020101
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Abstract: We formulate the measure analogue of generically stable types in first order theories with $ NIP$ (without the independence property), giving several characterizations, answering some questions from an earlier paper by Hrushovski and Pillay, and giving another treatment of uniqueness results from the same paper. We introduce a notion of ``generic compact domination'', relating it to stationarity of the Keisler measures, and also giving definable group versions. We also prove the ``approximate definability'' of arbitrary Borel probability measures on definable sets in the real and $ p$-adic fields.


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Additional Information

Ehud Hrushovski
Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel

Anand Pillay
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

Pierre Simon
Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel

DOI: https://doi.org/10.1090/S0002-9947-2012-05626-1
Received by editor(s): June 7, 2010
Received by editor(s) in revised form: May 10, 2011
Published electronically: December 13, 2012
Additional Notes: The first author was supported by ISF grant 1048/07
The second author was supported by a Marie Curie Chair EXC 024052 and EPSRC grant EP/F009712/1
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.