Let Xn have characteristic function n Find a counterexample to show that it is not enough to assume n(t) converges (pointwise in t) to a function (t) in order to conclude that Xn converges in distribution ...

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Let Xn have characteristic function n. Find a counterexample to show that it is not enough to

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Let Xn have characteristic function ζn. Find a counterexample to show that it is not enough to assume ζn(t) converges (pointwise in t) to a function

ζ(t) in order to conclude that Xn converges in distribution.

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