KnowraBoole's inequalityLinked fromLinked fromThe 16 pages that link to Boole's inequality, each with the reason it gives.All 16Related 9Compared with 7Almost sure convergenceRelated: It bounds probabilities of future error events when proving almost sure convergence.Inclusion–exclusion principleCompared with: It keeps only the first positive term, unlike the exact alternating expansion.Borel–Cantelli lemmaRelated: Applied to event tails, it yields the first lemma's convergence bound.Markov's inequalityCompared with: It also gives an assumption-light upper bound, but combines event probabilities rather than expectations.Probabilistic methodRelated: Bounding the chance of any failure can show that at least one outcome avoids every failure.Chernoff boundRelated: It extends individual Chernoff estimates to simultaneous control over many events.Coupon collector's problemRelated: It gives a simple bound on the chance that at least one type remains unseen.Concentration inequalityCompared with: It combines existing tail estimates but does not derive concentration for one quantity.Hoeffding's inequalityRelated: It extends single-deviation bounds to simultaneous control across many quantities.Probability axiomsRelated: It is a direct consequence of countable subadditivity.Bonferroni inequalitiesCompared with: It gives a broad upper bound, while Bonferroni truncations also supply lower bounds.Lovász local lemmaCompared with: Unlike the union bound, the lemma can certify avoidance when dependencies make a direct sum bound too weak.Johnson–Lindenstrauss lemmaRelated: Applying it to all point pairs turns individual distance guarantees into a simultaneous one.Kolmogorov's inequalityCompared with: Unlike a direct union bound, Kolmogorov's estimate avoids summing separate threshold probabilities.Azuma's inequalityRelated: It extends fixed-time Azuma bounds to several times or several martingales.Law of Truly Large NumbersCompared with: It bounds the chance of any occurrence without requiring independent trials.
KnowraBoole's inequalityLinked fromLinked fromThe 16 pages that link to Boole's inequality, each with the reason it gives.All 16Related 9Compared with 7Almost sure convergenceRelated: It bounds probabilities of future error events when proving almost sure convergence.Inclusion–exclusion principleCompared with: It keeps only the first positive term, unlike the exact alternating expansion.Borel–Cantelli lemmaRelated: Applied to event tails, it yields the first lemma's convergence bound.Markov's inequalityCompared with: It also gives an assumption-light upper bound, but combines event probabilities rather than expectations.Probabilistic methodRelated: Bounding the chance of any failure can show that at least one outcome avoids every failure.Chernoff boundRelated: It extends individual Chernoff estimates to simultaneous control over many events.Coupon collector's problemRelated: It gives a simple bound on the chance that at least one type remains unseen.Concentration inequalityCompared with: It combines existing tail estimates but does not derive concentration for one quantity.Hoeffding's inequalityRelated: It extends single-deviation bounds to simultaneous control across many quantities.Probability axiomsRelated: It is a direct consequence of countable subadditivity.Bonferroni inequalitiesCompared with: It gives a broad upper bound, while Bonferroni truncations also supply lower bounds.Lovász local lemmaCompared with: Unlike the union bound, the lemma can certify avoidance when dependencies make a direct sum bound too weak.Johnson–Lindenstrauss lemmaRelated: Applying it to all point pairs turns individual distance guarantees into a simultaneous one.Kolmogorov's inequalityCompared with: Unlike a direct union bound, Kolmogorov's estimate avoids summing separate threshold probabilities.Azuma's inequalityRelated: It extends fixed-time Azuma bounds to several times or several martingales.Law of Truly Large NumbersCompared with: It bounds the chance of any occurrence without requiring independent trials.