Finding generically stable measures

We discuss two constructions for obtaining generically stable Keisler measures in an NIP theory. First, we show how to symmetrize an arbitrary invariant measure to obtain a generically stable one from it. Next, we show that suitable sigma-additive probability measures give rise to generically stable measures. Also included is a proof that generically stable measures over o-minimal theories and the p-adics are smooth

An approximation of Keisler measure by using Morley sequences (Model theoretic aspects of the notion of independence and dimension)

We discuss on the Vapnik-Chervonenkis inequality in a stable structure following [1] and [2]. Some proofs may be modified but the results are essentially the same

On some dynamical aspects of NIP theories

We study some dynamical aspects of the action of automorphisms in model theory in particular in the presence of invariant measures. We give some characterizations for NIP theories in terms of dynamics of automorphisms and invariant measures for example in terms of compact systems, entropy and measure algebras. Moreover, we study the concept of symbolic representation for models. Amongst the results, we give some characterizations for dividing lines and combinatorial configurations such as independence property, order property and strictly order property in terms of symbolic representations