正上鞅及其诱导出的集函数

正上鞅及其诱导出的集函数 POSITIVE SUPERMARTINGALES AND THEIR INDUCED SET FUNCTIONS 甘师信 Gan Shixin and Tong Guangrong first-author 童光荣 文献[1]、[2] ,[3]讨论了正鞅诱导出的集函数的σ可加性及绝对连续性。本文对正上鞅诱导出的集函数讨论了同样的问题,给出了正上鞅诱导出的集函数σ可加性及绝对连续性的充要条件,此处还讨论了序列弱L 1 收敛的等价表述,用正上鞅诱导出的集函数给出了正上鞅一致可积的充要条件。 [1]、[2] and [3] deal with σ-additivity and absolute contiguity of the set functions induced by positive martingales. In this paper we discuss the similar problems for the set functions induced by positive supermartingales, Necessary and sufficient conditions are given for σ-additivity and absolute continuity of the set functions induced by positive supermartingales. in the other direction Uniform iniegrability of positive supermastingales is Charaterized in terms of the set functions induced by the positive supermartingales. 中国科学院科学基金 1986-03-01 2021-04-01 3