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Boole's inequality — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Boole%27s_inequality
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T18:27:22.233Z
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Boole's inequality — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Boole%27s_inequality (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_798508a6727c (Metraipolis archive dc_798508a6727c, sha256 903f49df73d1b47bef577a7c79d944e97d66e1bc918453c17ee8f0c5bc46611e)

BibTeX

@misc{dc798508a6727c,
  title = {Boole's inequality — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Boole%27s_inequality},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_798508a6727c; sha256 903f49df73d1b47bef577a7c79d944e97d66e1bc918453c17ee8f0c5bc46611e},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Boole%27s_inequality. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. Formally, for a countable set of events A1, A2, A3, ..., we have P ( ⋃ i = 1 ∞ A i ) ≤ ∑ i = 1 ∞ P ( A i ) . {\displaystyle {\mathbb {P} }\left(\bigcup _{i=1}^{\infty }A_{i}\right)\leq \sum _{i=1}^{\infty }{\mathbb {P} }(A_{i}).} In measure-theoretic terms, Boole's inequality is an instance of the countable subadditivity of measures. Consequently, it holds not only for probability measures P {\displaystyle {\mathbb {P} }} , but for arbitrary measures. Boole's inequality is named after George Boole.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «probability theory»).
Fonte: Wikipedia in inglese, voce «Boole's inequality» — https://en.wikipedia.org/wiki/Boole%27s_inequality
Wikidata Q517378 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q517378
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Boole%27s_inequality?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1374748492, consultata il 2026-10-15T17:56:14.683Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 9cb3fd39ed560d38177b8ab21792ee4f2665c52234e38c1d7f0d19aa82c5a6c9