Merging with a set of probability measures: A characterization
刻画了先验概率弱合并一组概率测度的条件，引入条件规则概念，证明可学习性等价于可数族条件规则的最终生成，并推广到重复博弈。
In this paper, I provide a characterization of a \\textit{set} of probability measures with which a prior ``weakly merges.'' In this regard, I introduce the concept of ``conditioning rules'' that represent the \\textit{regularities% } of probability measures and define the ``eventual generation'' of probability measures by a family of conditioning rules. I then show that a set of probability measures is learnable (i.e., all probability measures in the set are weakly merged by a prior) if and only if all probability measures in the set are eventually generated by a \\textit{countable} family of conditioning rules. I also demonstrate that quite similar results are obtained with ``almost weak merging.'' In addition, I argue that my characterization result can be extended to the case of infinitely repeated games and has some interesting applications with regard to the impossibility result in Nachbar (1997, 2005).