A simple proof of Blackwell’s theorem on the comparison of experiments for a general state space
针对一般状态空间，给出了布莱克威尔充分性与Bohnenblust–Shapley–Sherman信息量更多准则等价性的简单证明，仅依赖紧集的有限交性质，并举例说明Boll定义的脆弱性。
This paper offers, for a general state space, a simple proof of the equivalence between Blackwell sufficiency and the Bohnenblust–Shapley–Sherman criterion of more-informativeness . The proof relies on nothing more than the finite intersection property of compact sets. While several proofs exist for finite state spaces, infinite spaces, as necessitated in applications with continuous distributions, is explored by Boll (1955), Amershi (1988) (but for a finite-dimensional action set), and reviewed in LeCam’s foundational rubric for the subject. We offer two examples to show the fragility of Boll’s definition of the second criterion, and the necessity of his assumption of absolute continuity. • A simple proof of Blackwell’s Theorem for experiments set in a general state space. • A counterexample to the theorem under Boll’s formulation of more-informativeness . • An example showing that in general Boll’s domination assumption cannot be eliminated.