KnowraPortmanteau theoremLinked fromLinked fromThe 8 pages that link to Portmanteau theorem, each with the reason it gives.All 8Broader topic 1Related 7Convergence in probabilityRelated: It clarifies what distributional convergence says—and what it does not say—about probability limits.Convergence in distributionRelated: It connects distributional convergence to inequalities for closed and open sets.Weak convergenceRelated: It translates test-function convergence into conditions involving closed sets, open sets, and distribution functions.Prokhorov's theoremRelated: Its closed-set inequalities help connect tightness to weak limits.Continuous mapping theoremRelated: Its distributional convergence framework supports rigorous versions of the theorem.Lévy's continuity theoremRelated: It supplies alternative tests for the convergence established here.Fatou's lemmaBroader topic: Its lower-bound condition for lower semicontinuous functions is an integral form of Fatou's principle.Skorokhod representation theoremRelated: Its criteria describe the convergence assumption used in the representation result.