Word.ws English Dictionary

σ-algebra

/ˈsɪɡ.mə ˈæl.dʒɪ.bɹə/

σ-algebra noun: a collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions.

Noun

σ-algebra (plural σ-algebras)

  1. A collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions.
    • Consider all the sigma-algebras that contain #92;mathcal#123;F#125; and take their intersection, which we call #92;Sigma, i.e., a subset A#92;subset#92;Omega is in #92;Sigma if and only if A is in every sigma-algebra containing #92;mathcal#123;F#125;. It is easy to check that #92;Sigma is indeed a...2001, Elliott H. Lieb, Michael Loss, Analysis, American Mathematical Society, page 4
    • Consider all the σ-algebras on [0,1] containing all intervals from that segment (there is at least one such σ-algebra, for the collection of all the subsets of a given set clearly forms a σ-algebra).2013, Alexandr A. Borovkov, Probability Theory, Springer, page 15
    Synonyms:
    σ-field

Synonyms of σ-algebra

  • σ-field

Forms of σ-algebra

pluralσ-algebras
alternative formsigma-algebra
alternative formΣ-algebra

Phrases with σ-algebra

Questions about σ-algebra

What does σ-algebra mean?
Σ-algebra means a collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions.
What part of speech is σ-algebra?
Σ-algebra is a noun.
How do you pronounce σ-algebra?
Σ-algebra is pronounced /ˈsɪɡ.mə ˈæl.dʒɪ.bɹə/.
What is the plural of σ-algebra?
The plural of σ-algebra is σ-algebras.

Words near σ-algebra in the dictionary

  1. π-on
  2. π-system
  3. π-systems
  4. πon
  5. σ-additivity
  6. σ-algebra
  7. σ-algebras
  8. σ-compact
  9. σ-finite measure
  10. σ-finite measures
  11. χ² distribution

Source and license

Adapted from Wiktionary: σ-algebra (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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