I know the definition of vague convergence as Definition: Let F n </msub> be distrib

ga2t1a2dan1oj

ga2t1a2dan1oj

Answered question

2022-05-14

I know the definition of vague convergence as
Definition: Let F n be distribution functions. F n F if for every finite interval I of continuity points of F F n ( I ) F ( I ).
That is the definition I got from my professor who pointed out that the measure defined by F may not be a probability measure but I can't imagine a counterexample to that fact.

Answer & Explanation

empatteMattmkezo

empatteMattmkezo

Beginner2022-05-15Added 22 answers

Hint: consider the measures δ n that give mass 1 to set in the real line that contains the point n, and mass 0 otherwise. That is, δ n is a probability measure concentrated at { n }. You can see that the sequence converges to 0 vaguely.

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