2021/09/24 by Khanaki, Karim
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2109.11973
We introduce the notion of dependence, as a property of a Keisler measure, and generalize several results of [HPS13] on generically stable measures (in NIP theories) to arbitrary theories. Among other things, we show that this notion is very natural and fundamental for several reasons: (i) all measures in NIP theories are dependent, (ii) all types and all fim measures in any theory are dependent, and (iii) as a crucial result in measure theory, the Glivenko-Cantelli class of functions (formulas) is characterized by dependent measures.