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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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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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    I was going to write Prof Billingsley. Sadly, he died recently.2011-06-08