Geodesic
On NIP and invariant measures
Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 1005-1061

Voir la notice de l'article provenant de la source EMS Press

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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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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