Geodesic
On NIP and invariant measures
Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 1005-1061
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We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of the paper [16]. Among key results are (i) if p=tp(b/A) does not fork over A then the Lascar strong type of b over A coincides with the compact strong type of b over A and any global nonforking extension of p is Borel definable over bdd(A), (ii) analogous statements for Keisler measures and definable groups, including the fact that G000=G00 for G definably amenable, (iii) definitions, characterizations and properties of “generically stable” types and groups, (iv) uniqueness of invariant (under the group action) Keisler measures on groups with finitely satisfiable generics, (v) a proof of the compact domination conjecture for (definably compact) commutative groups in o-minimal expansions of real closed fields.
DOI : 10.4171/jems/274
Classification : 12-XX, 20-XX, 00-XX 
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     author = {Ehud Hrushovski and Anand Pillay},
     title = {On {NIP} and invariant measures},
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     pages = {1005--1061},
     year = {2011},
     volume = {13},
     number = {4},
     doi = {10.4171/jems/274},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/274/}
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Ehud Hrushovski; Anand Pillay. On NIP and invariant measures. Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 1005-1061. doi: 10.4171/jems/274

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