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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).

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up vote 1 down vote accepted

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.

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Oh, yes! The notorious Jean-Pierre Portmanteau, Espoir pour l'ensemble vide, Annales de l'Université de Felletin CXLI (1915), 322-325. Now that you mention Billingsley's book, I remember... – t.b. Jun 7 '11 at 0:15
BTW, Billingsley's book is so good you could eat it with great vanilla ice cream and chocolate sauce. It is a glorious mathematics book with few peers. Its clarity and coherence are the work of a true intellect of the highest order. – ncmathsadist Jun 7 '11 at 0:30
A marvelous play on words is underway here..... – ncmathsadist Jun 7 '11 at 0:38
So.... did the late Prof. Billingsley give it that name himself? – Michael Hardy Jun 7 '11 at 1:33
I was going to write Prof Billingsley. Sadly, he died recently. – ncmathsadist Jun 8 '11 at 21:51

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