We show that the sequential closure of a family of probability measures on the canonical space of càdlàg paths satisfying Stricker’s uniform tightness condition is a weak^∗ compact set of semimartingale measures in the dual pairing of bounded continuous functions and Radon measures, that is, the dual pairing from the Riesz representation theorem under topological assumptions on the path space. Similar results are obtained for quasi- and supermartingales under analogous conditions. In particular, we give a full characterisation of the strongest topology on the Skorokhod space for which these results are true.

中文翻译：

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半ies的Riesz表示定理和弱*紧性

我们证明，在满足连续连续函数和Radon度量对的对中，满足Stricker一致紧性条件的càdlàg路径的规范空间上的概率测度序列的顺序闭合是一个弱^＊紧集在路径空间的拓扑假设下根据Riesz表示定理进行配对。在类似条件下，准超市和超级超市也获得了类似的结果。特别是，我们对Skorokhod空间上最强的拓扑进行了完整的表征，得出了这些结果。