paper

A note on generically stable measures and fsg groups

arXiv:1105.2780 · doi:10.1215/00294527-1814705

Abstract

We prove that if Î¼is a generically stable stable measure in a first order theory with NIP and mu(Ï(x,b)) = 0 for all b, then Î¼^{(n)}(\exists y(Ï(x_1,y)\wedge ... \wedge Ï(x_n,y))) = 0. We deduce that if G is an fsg grooup then a definable subset X of G is generic just if every translate of X does not fork over \emptyset.

8 pages