Generically stable and smooth measures in NIP theories
By Ehud Hrushovski, Anand Pillay, Pierre Simon. 2010
56 citations recorded by the source corpus.
We formulate the measure analogue of generically stable types in first order theories with NIP (without the independence property), giving several characterizations, answering some questions from [9], and giving another treatment of uniqueness results from [9]. We introduce a notion of “generic compact domination”, relating it to stationarity of Keisler measures, and also giving group versions. We also prove the “approximate definability” of arbitrary Borel probability measures on definable sets in the real and p-adic fields.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/80866965cc02568cbd8fca473a2c363bfdf4787d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Geometry and Topology
- Ehud Hrushovski
- Terence Tao
- Emmanuel Breuillard
- Ben Joseph Green
- László Pyber
- E. Szab'o
- Ernie Croot
- Olof Sisask
Citations in the corpus
- Stable group theory and approximate subgroups (2009, background): “e over M, meaning that µi(φ(x,b)) is a Borel function of tp(b/M). Assume the µi commute, in the sense that for any i6= j∈ Υ, for any formula φ(xi,xj) over M, Z µj(φ(xi,xj))dµi = Z µi(φ(xi,xj))dµj see [27]. Any measures obtained as ultraproducts of counting measures will certainly have this property.”