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Statements

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dbr:Proofs_of_convergence_of_random_variables
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yago:PsychologicalFeature100023100 yago:Abstraction100002137 yago:WikicatArticleProofs yago:Information105816287 yago:Evidence105823932 yago:Proof105824739 yago:Cognition100023271
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Proofs of convergence of random variables
rdfs:comment
This article is supplemental for “Convergence of random variables” and provides proofs for selected results. Several results will be established using the portmanteau lemma: A sequence {Xn} converges in distribution to X if and only if any of the following conditions are met: 1. * E[f(Xn)] → E[f(X)] for all bounded, continuous functions f; 2. * E[f(Xn)] → E[f(X)] for all bounded, Lipschitz functions f; 3. * limsup{Pr(Xn ∈ C)} ≤ Pr(X ∈ C) for all closed sets C;
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This article is supplemental for “Convergence of random variables” and provides proofs for selected results. Several results will be established using the portmanteau lemma: A sequence {Xn} converges in distribution to X if and only if any of the following conditions are met: 1. * E[f(Xn)] → E[f(X)] for all bounded, continuous functions f; 2. * E[f(Xn)] → E[f(X)] for all bounded, Lipschitz functions f; 3. * limsup{Pr(Xn ∈ C)} ≤ Pr(X ∈ C) for all closed sets C;
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dbr:Convergence_of_random_variables
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wikipedia-en:Proofs_of_convergence_of_random_variables
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