A Simple Characterization of Stochastically Monotone Functions
证明，随机单调函数等价于可加分离成严格递增分量的函数，从而简化了McKelvey和Page关于共同知识的一个著名定理的条件。
MCKELVEY AND PAGE (1986) proved a remarkable theorem on common knowledge. Suppose n individuals start with a common prior and then form conditional probabilities of some event of interest based on their different information. If a stochastically monotone aggregate of the n conditional probabilities is common knowledge, then the assessments must be identical. We show that the aggregation of individual assessments allowed for in the theorem admits an elementary characterization: a function is stochastically monotone if and only if it is additively separable into strictly increasing components