2009/07/26 by Itaï Ben Yaacov, Yaacov, Itaï Ben, Alexander Berenstein +3
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.0907.4508
arxiv created 2013/08/06 · arxiv updated 2013/08/07
We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes & Rosenthal \citeBerkes-Rosenthal:AlmostExchangeableSequences. In order to do this, itemize We study and compare three notions of convergence of types in a stable theory: logic convergence, i.e., formula by formula, metric convergence (both already well studied) and convergence of canonical bases. In particular, we characterise ℵ0-categorical stable theories in which the last two agree. We characterise sequences which admit almost indiscernible sub-sequences. We apply these tools to ARV, the theory (atomless) random variable spaces. We characterise types and notions of convergence of types as conditional distributions and weak/strong convergence thereof, and obtain, among other things, the Main Theorem of Berkes & Rosenthal. itemize