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- Proofs_of_convergence_of_random_variables abstract "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: E[f(Xn)] → E[f(X)] for all bounded, continuous functions f; E[f(Xn)] → E[f(X)] for all bounded, Lipschitz functions f; limsup{Pr(Xn ∈ C)} ≤ Pr(X ∈ C) for all closed sets C;".
- Proofs_of_convergence_of_random_variables wikiPageID "24334988".
- Proofs_of_convergence_of_random_variables wikiPageLength "13264".
- Proofs_of_convergence_of_random_variables wikiPageOutDegree "13".
- Proofs_of_convergence_of_random_variables wikiPageRevisionID "679107359".
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Borel–Cantelli_lemma.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Bounded_function.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Category:Article_proofs.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Category:Probability_theory.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Closed_set.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Continuous_function.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Convergence_of_measures.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Convergence_of_random_variables.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Cumulative_distribution_function.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Indicator_function.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Limit_superior_and_limit_inferior.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Limsup.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Lipschitz_continuity.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Lipschitz_function.
- Proofs_of_convergence_of_random_variables wikiPageWikiLink Portmanteau_lemma.
- Proofs_of_convergence_of_random_variables wikiPageWikiLinkText "Proofs of convergence of random variables".
- Proofs_of_convergence_of_random_variables wikiPageWikiLinkText "[proof]".
- Proofs_of_convergence_of_random_variables hasPhotoCollection Proofs_of_convergence_of_random_variables.
- Proofs_of_convergence_of_random_variables wikiPageUsesTemplate Template:Anchor.
- Proofs_of_convergence_of_random_variables wikiPageUsesTemplate Template:Cite_book.
- Proofs_of_convergence_of_random_variables wikiPageUsesTemplate Template:No_footnotes.
- Proofs_of_convergence_of_random_variables wikiPageUsesTemplate Template:Refbegin.
- Proofs_of_convergence_of_random_variables wikiPageUsesTemplate Template:Refend.
- Proofs_of_convergence_of_random_variables subject Category:Article_proofs.
- Proofs_of_convergence_of_random_variables subject Category:Probability_theory.
- Proofs_of_convergence_of_random_variables type Article.
- Proofs_of_convergence_of_random_variables type Article.
- Proofs_of_convergence_of_random_variables type Proof.
- Proofs_of_convergence_of_random_variables 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: E[f(Xn)] → E[f(X)] for all bounded, continuous functions f; E[f(Xn)] → E[f(X)] for all bounded, Lipschitz functions f; limsup{Pr(Xn ∈ C)} ≤ Pr(X ∈ C) for all closed sets C;".
- Proofs_of_convergence_of_random_variables label "Proofs of convergence of random variables".
- Proofs_of_convergence_of_random_variables sameAs m.07s3pw2.
- Proofs_of_convergence_of_random_variables sameAs Q7250031.
- Proofs_of_convergence_of_random_variables sameAs Q7250031.
- Proofs_of_convergence_of_random_variables wasDerivedFrom Proofs_of_convergence_of_random_variables?oldid=679107359.
- Proofs_of_convergence_of_random_variables isPrimaryTopicOf Proofs_of_convergence_of_random_variables.