Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
almost sure convergence
|
| gptkbp:concerns |
measure theory
infinite sequence of events |
| gptkbp:field |
gptkb:probability_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Borel–Cantelli lemma
|
| gptkbp:namedAfter |
gptkb:Francesco_Paolo_Cantelli
gptkb:Émile_Borel |
| gptkbp:publishedIn |
gptkb:Comptes_Rendus_de_l'Académie_des_Sciences
|
| gptkbp:relatedTo |
gptkb:Kolmogorov_zero–one_law
gptkb:law_of_large_numbers |
| gptkbp:state |
If the events are independent and the sum of their probabilities diverges, then the probability that infinitely many of them occur is one.
If the sum of the probabilities of events is finite, then the probability that infinitely many of them occur is zero. |
| gptkbp:yearProposed |
1909
|
| gptkbp:bfsParent |
gptkb:Probability_theory
gptkb:Émile_Borel gptkb:Kolmogorov's_zero–one_law gptkb:Lévy's_zero–one_law gptkb:0-1_law |
| gptkbp:bfsLayer |
6
|