What’s the right proof of the Continuous Mapping Theorem?
Read OriginalThis technical article analyzes the Continuous Mapping Theorem in probability theory, which deals with the convergence of transformed random variables. It compares three known proof approaches: the classic method using CDFs, the modern standard using bounded continuous functions and the Portmanteau Lemma, and a method using almost-sure representations (Skorohod's theorem). The author discusses the trade-offs in complexity and insight, advocating for the pedagogical value of the representation-based proof despite its apparent overkill.
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