Ben Smith digs into a theorem:
The Portmanteau Theorem provides a set of equivalences of weak convergence that still remains relevant for establishing asymptotic results in probability and statistics. While the theory around weak convergence is well developed, I was inspired to put together a writeup proving all the equivalences in a self contained manner, by first presenting the relevant theorems applied (without proving them) along with along with a visual on the implication cycle created for the proof and some discussion about other presentations available in popular textbooks and some historical notes.
Click through for the PDF.