The Riesz representation theorem and weak∗ compactness of semimartingales
证明了在càdlàg路径空间上满足Stricker一致紧性条件的概率测度族的序列闭包是弱*紧的半鞅测度集，并给出了Skorokhod空间上使该结果成立的最强拓扑的完整刻画。
Abstract 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.