几乎不可分辨列与标准基的收敛性
Almost indiscernible sequences and convergence of canonical bases
摘要：
我们给出了一个模型理论帐户的几个结果有关序列的随机变量出现在Berkes & Rosenthal \cite{Berkes-Rosenthal:AlmostExchangeableSequences}。为了做到这一点，我们研究并比较了稳定理论中类型收敛的三个概念：逻辑收敛，即，公式的公式，度量收敛（都已经很好地研究）和规范基的收敛。特别是，我们证明了$\aleph_0$ -范畴稳定的理论，其中最后两个同意。我们对承认几乎不可辨别的子序列的序列进行分类。我们将这些工具应用于$ARV$，理论（无原子）随机变量空间。我们将类型和类型的收敛概念定义为条件分布及其弱/强收敛，并得到了Berkes & Rosenthal的主要定理。[详细]
英文摘要：
We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes & Rosenthal \cite{Berkes-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 $\aleph_0$-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}
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