Dependent measures in independent theories
Abstract
We introduce the notion of dependence, as a property of a Keisler measure, and generalize several results of [HPS13] on generically stable measures (in theories) to arbitrary theories. Among other things, we show that this notion is very natural and fundamental for several reasons: (i) all measures in theories are dependent, (ii) all types and all 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.
Cite
@article{arxiv.2109.11973,
title = {Dependent measures in independent theories},
author = {Karim Khanaki},
journal= {arXiv preprint arXiv:2109.11973},
year = {2025}
}
Comments
23 pages, to appear in the journal ZML: https://zml.international/about (In this version, some statements-- including Theorem 5.2 from the previous version-- that are equivalent to known results and have essentially standard proofs have been removed.)