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1 results

  • ALMOST INDISCERNIBLE SEQUENCES AND CONVERGENCE OF CANONICAL BASES

  • ITAÏ BEN YAACOV, ALEXANDER BERENSTEIN, C. WARD HENSON
  • Journal:
    The Journal of Symbolic Logic / Volume 79 / Issue 2 / June 2014
    Published online by Cambridge University Press:
    25 June 2014, pp. 460-484
    Print publication:
    June 2014

  • We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes and Rosenthal [12]. In order to do this,

    • • 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 that admit almost indiscernible sub-sequences.

    • • We apply these tools to the theory of atomless random variables (ARV). 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 and Rosenthal.