### Chapter 10 Representations and couplings

2001-6-7 · 10.1 What is coupling? 239 <3> Example. Suppose {Pn} is a sequence of probability measures on the real line, for which Pn P. Write Fn and F for the corresponding distribution functions, and qn and q for the quantile functions. From Section 7.1 we know that Fn(x) F(x) at each x for which P{x}=0, which implies (Problem [1]) that qn(u) q(u) at

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