A note on generically stable measures and fsg groups

TL;DR

This paper explores properties of generically stable measures in NIP theories and characterizes generic subsets in fsg groups, establishing conditions for non-forking and measure zero results.

Contribution

It proves a new measure-theoretic property for generically stable measures and characterizes generic subsets in fsg groups via non-forking conditions.

Findings

Generically stable measures assign measure zero to certain formulas.

In fsg groups, a definable set is generic iff all its translates do not fork over the empty set.

The paper establishes a measure-theoretic criterion for genericity in groups.

Abstract

We prove that if \mu is a generically stable stable measure in a first order theory with NIP and mu(\phi(x,b)) = 0 for all b, then \mu^{(n)}(\exists y(\phi(x_1,y)\wedge ... \wedge \phi(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.