Where did the portmanteau theorem get its name? Does the portmanteau theorem relate to an actual portmanteau somehow? A portmanteau is either an item of luggage or a word that is a blend of two others (e.g. brunch= breakfast + lunch). More generally, where did the name for this theorem come from? My only conjecture is that in one part of its proof (at least the proof in _Ergodic Theory on Compact Spaces_ by Denker), it "blends together" the trivially equivalent statements $$\limsup P_{n}(C) \leq P(C) \text{ for every closed } C$$ and $$\liminf P_{n}(U) \geq P(U) \text{ for every open } U$$ in order to prove another condition follows from either (hence both).

This theorem shows that a whole bunch of conditions are equivalent. Hence, the term 'portmanteau' or large traveling trunk. See Billingsley's book Convergence of Probability Measures.