论文信息 - A Note on Generically Stable Measures and fsg Groups

A Note on Generically Stable Measures and fsg Groups

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.

[1] Annalisa Conversano,et al. Connected components of definable groups and o-minimality I , 2011 .

[2] Ya'acov Peterzil,et al. Groups, measures, and the NIP , 2006 .

[3] A. Pillay. Strong dependence, weight, and measure , 2010, 1005.0076.

[4] L. Newelski. Model theoretic aspects of the ellis semigroup , 2012 .

[5] Ehud Hrushovski,et al. Generically stable and smooth measures in NIP theories , 2010, 1002.4763.

[6] Anand Pillay,et al. Generic stability, regularity, and quasi-minimality , 2009 .

[7] Ehud Hrushovski,et al. On NIP and invariant measures , 2007, 0710.2330.