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Groups, measures, and the NIP
Author(s):
Ehud
Hrushovski;
Ya'acov
Peterzil;
Anand
Pillay
Journal:
J. Amer. Math. Soc.
21
(2008),
563-596.
MSC (2000):
Primary 03C68, 03C45, 22C05, 28E05
Posted:
February 2, 2007
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Additional information
Abstract:
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  in saturated  -minimal structures to compact Lie groups. We also prove some other structural results about such  , for example the existence of a left invariant finitely additive probability measure on definable subsets of  . 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  -minimal case.
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Additional 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
DOI:
10.1090/S0894-0347-07-00558-9
PII:
S 0894-0347(07)00558-9
Keywords:
$o$-minimal,
independence property,
compact Lie group,
Keisler measure.
Received by editor(s):
July 16, 2006
Posted:
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 of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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