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.Borel–Cantelli lemmaRelated: Applied to event tails, it yields the first lemma's convergence bound.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.Hoeffding's inequalityRelated: It extends single-deviation bounds to simultaneous control across many quantities.Probability axiomsRelated: It is a direct consequence of countable subadditivity.Johnson–Lindenstrauss lemmaRelated: Applying it to all point pairs turns individual distance guarantees into a simultaneous one.Azuma's inequalityRelated: It extends fixed-time Azuma bounds to several times or several martingales.