KnowraBorel–Cantelli lemmaLinked fromLinked fromThe 18 pages that link to Borel–Cantelli lemma, each with the reason it gives.All 18Related 17Narrower topic 1Law of large numbersRelated: Its first part helps turn probability bounds into almost-sure convergence in strong-law proofs.Almost sure convergenceRelated: Summable probabilities of large errors ensure that only finitely many such errors occur almost surely.Convergence in probabilityRelated: It connects summable error probabilities to almost-sure convergence, a stronger mode.Émile BorelRelated: Its name reflects Borel’s foundational work linking measure and probability.Strong law of large numbersRelated: The lemma's first form underlies classical arguments proving almost-sure limits.Almost-everywhere convergenceRelated: Its first lemma often proves almost-everywhere convergence by making error events summable.Kolmogorov's three-series theoremRelated: Its first lemma controls how often terms exceed the truncation threshold.Law of the iterated logarithmRelated: They are standard tools for turning tail bounds into almost-sure fluctuation statements.Kolmogorov continuity theoremRelated: Applying it across finer grids turns increment tail bounds into almost-sure path control.Kolmogorov's zero–one lawRelated: Independence can make the event of infinitely many occurrences a tail event with probability zero or one.Skorokhod representation theoremRelated: It is often used to derive almost-sure convergence from probability bounds, a different route than representation.Glivenko–Cantelli theoremRelated: It can turn summable deviation bounds into almost-sure convergence.Kolmogorov's inequalityRelated: Summable maximal bounds imply that large partial-sum deviations occur only finitely often.Kolmogorov's two-series theoremRelated: Probability bounds on excursions can yield eventual control through Borel–Cantelli.Kronecker's lemmaRelated: Probability proofs using the lemma often combine series bounds with almost-sure event control.Infinite monkey theoremRelated: It formalizes why repeated independent opportunities eventually yield the text.Law of Truly Large NumbersNarrower topic: It formalizes when recurring opportunities produce infinitely many occurrences, a stronger claim than occurring once.Lochs's theoremRelated: Measure-theoretic control of exceptional sets supports almost-sure asymptotic statements.
KnowraBorel–Cantelli lemmaLinked fromLinked fromThe 18 pages that link to Borel–Cantelli lemma, each with the reason it gives.All 18Related 17Narrower topic 1Law of large numbersRelated: Its first part helps turn probability bounds into almost-sure convergence in strong-law proofs.Almost sure convergenceRelated: Summable probabilities of large errors ensure that only finitely many such errors occur almost surely.Convergence in probabilityRelated: It connects summable error probabilities to almost-sure convergence, a stronger mode.Émile BorelRelated: Its name reflects Borel’s foundational work linking measure and probability.Strong law of large numbersRelated: The lemma's first form underlies classical arguments proving almost-sure limits.Almost-everywhere convergenceRelated: Its first lemma often proves almost-everywhere convergence by making error events summable.Kolmogorov's three-series theoremRelated: Its first lemma controls how often terms exceed the truncation threshold.Law of the iterated logarithmRelated: They are standard tools for turning tail bounds into almost-sure fluctuation statements.Kolmogorov continuity theoremRelated: Applying it across finer grids turns increment tail bounds into almost-sure path control.Kolmogorov's zero–one lawRelated: Independence can make the event of infinitely many occurrences a tail event with probability zero or one.Skorokhod representation theoremRelated: It is often used to derive almost-sure convergence from probability bounds, a different route than representation.Glivenko–Cantelli theoremRelated: It can turn summable deviation bounds into almost-sure convergence.Kolmogorov's inequalityRelated: Summable maximal bounds imply that large partial-sum deviations occur only finitely often.Kolmogorov's two-series theoremRelated: Probability bounds on excursions can yield eventual control through Borel–Cantelli.Kronecker's lemmaRelated: Probability proofs using the lemma often combine series bounds with almost-sure event control.Infinite monkey theoremRelated: It formalizes why repeated independent opportunities eventually yield the text.Law of Truly Large NumbersNarrower topic: It formalizes when recurring opportunities produce infinitely many occurrences, a stronger claim than occurring once.Lochs's theoremRelated: Measure-theoretic control of exceptional sets supports almost-sure asymptotic statements.