On NIP and invariant measures

Hrushovski, Ehud, and Pillay, Anand. "On NIP and invariant measures." Journal of the European Mathematical Society 013.4 (2011): 1005-1061. <http://eudml.org/doc/277262>.

@article{Hrushovski2011,
abstract = {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 $p=\operatorname\{tp\}(b/A)$ 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 $\operatorname\{bdd\}(A)$, (ii) analogous statements for Keisler measures and definable groups, including the fact that $G^\{000\}=G^\{00\}$ 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.},
author = {Hrushovski, Ehud, Pillay, Anand},
journal = {Journal of the European Mathematical Society},
keywords = {Lascar strong types; Keisler measures; definable groups; NIP; $o$-minimal expansions of real closed fields; forking; Lascar strong types; Keisler measures; definable groups; NIP; o-minimal expansions of real closed fields},
language = {eng},
number = {4},
pages = {1005-1061},
publisher = {European Mathematical Society Publishing House},
title = {On NIP and invariant measures},
url = {http://eudml.org/doc/277262},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Hrushovski, Ehud
AU - Pillay, Anand
TI - On NIP and invariant measures
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 4
SP - 1005
EP - 1061
AB - 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 $p=\operatorname{tp}(b/A)$ 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 $\operatorname{bdd}(A)$, (ii) analogous statements for Keisler measures and definable groups, including the fact that $G^{000}=G^{00}$ 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.
LA - eng
KW - Lascar strong types; Keisler measures; definable groups; NIP; $o$-minimal expansions of real closed fields; forking; Lascar strong types; Keisler measures; definable groups; NIP; o-minimal expansions of real closed fields
UR - http://eudml.org/doc/277262
ER -