On ws-convergence of product measures

• 成果类型: Article
• 署名作者: Balder, EJ
• 署名单位: Utrecht University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.26.3.494.10581
• 发表日期: 2001
• 页码: 494-518
• 关键词: sequential-compactness; EXISTENCE; THEOREM; SPACES; lemma

摘要

A number of fundamental results, centered around extensions of Prohorov's theorem, is proven for the ws-topology for measures on a product space. These results contribute to die foundations of stochastic decision theory. They also subsume the principal results of Young measure theory, which only considers product measures with a fixed, common marginal. Specializations yield the criterion for relative ws-compactness of Schal (1975), the refined characterizations of ws-convergence of Galdeano and Truffert (1997, 1998), and a new version of Fatou's lemma in several dimensions. In a separate, nonsequential development, a generalization is given of the relative ws-compactness criterion of Jacod and Memin (1981). New applications are given to the existence of optimal equilibrium distributions over player-action pairs in game theory and the existence of most optimistic scenarios in stochastic decision theory.