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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Groups, measures, and the NIP
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by Ehud Hrushovski, Ya’acov Peterzil and Anand Pillay
J. Amer. Math. Soc. 21 (2008), 563-596
Published electronically: February 2, 2007


We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author’s conjectures relating definably compact groups $G$ in saturated $o$-minimal structures to compact Lie groups. We also prove some other structural results about such $G$, for example the existence of a left invariant finitely additive probability measure on definable subsets of $G$. We finally introduce the new notion of “compact domination" (domination of a definable set by a compact space) and raise some new conjectures in the $o$-minimal case.
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Bibliographic Information
  • Ehud Hrushovski
  • Affiliation: Hebrew University of Jerusalem, Department of Mathematics, Jerusalem, Israel
  • Ya’acov Peterzil
  • Affiliation: University of Haifa, Department of Mathematics and Computer Science, Haifa, Israel
  • Anand Pillay
  • Affiliation: University of Illinois, Department of Mathematics, Altgeld Hall, 1409 W Green Street Urbana, IL 61801, and University of Leeds, School of Mathematics, Leeds, LS2 9JT England
  • MR Author ID: 139610
  • Received by editor(s): July 16, 2006
  • Published electronically: February 2, 2007
  • Additional Notes: The first author was supported by the Israel Science Foundation grant no. 244/03
    The last author was supported by NSF grants DMS-0300639 and FRG DMS-0100979, as well as a Marie Curie chair
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 21 (2008), 563-596
  • MSC (2000): Primary 03C68, 03C45, 22C05, 28E05
  • DOI:
  • MathSciNet review: 2373360