Thomas Lumley 5/3/2015

What’s the right proof of the Continuous Mapping Theorem?

Read Original

This 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.

What’s the right proof of the Continuous Mapping Theorem?

Comments

No comments yet

Be the first to share your thoughts!