"σ-algebra" meaning in English

See σ-algebra in All languages combined, or Wiktionary

Noun

IPA: /ˈsɪɡ.mə ˈæl.dʒɪ.bɹə/ Forms: σ-algebras [plural]
Head templates: {{en-noun|σ-algebras|head=σ-algebra}} σ-algebra (plural σ-algebras)
  1. (mathematical analysis) 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. Wikipedia link: Sigma-algebra Categories (topical): Mathematical analysis, Measure theory Synonyms: sigma-algebra, Σ-algebra Synonyms (collection of subsets that obeys certain conditions): σ-field Hypernyms (collection of subsets that obeys certain conditions): field of sets, set algebra Hyponyms (collection of subsets that obeys certain conditions): Borel σ-algebra, μ-completion Holonyms: measurable space Meronyms: measurable set Related terms: σ-ring Translations (Translations): tribu [feminine] (French), σ-algèbre [feminine] (French), σ-Algebra [feminine] (German), σ-алгебра (σ-algebra) [feminine] (Russian)

Inflected forms

Download JSON data for σ-algebra meaning in English (5.0kB)

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          "ref": "2001, Elliott H. Lieb, Michael Loss, Analysis, American Mathematical Society, page 4",
          "text": "Consider all the sigma-algebras that contain #x5C;mathcal#x7B;F#x7D; and take their intersection, which we call #x5C;Sigma, i.e., a subset A#x5C;subset#x5C;Omega is in #x5C;Sigma if and only if A is in every sigma-algebra containing #x5C;mathcal#x7B;F#x7D;. It is easy to check that #x5C;Sigma is indeed a sigma-algebra.",
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          "ref": "2017 February 4, Marco Taboga, Lectures on Probability Theory and Mathematical Statistics, 2nd edition, San Bernardino, CA, USA, §10.5.1, page 75",
          "text": "Denote by #x5C;mathcal#x7B;F#x7D; the set of subsets of [the sample space] Ω which are considered events. #x5C;mathcal#x7B;F#x7D; is called the space of events. In rigorous probability theory, #x5C;mathcal#x7B;F#x7D; is required to be a sigma-algebra on Ω.",
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-06-04 from the enwiktionary dump dated 2024-05-02 using wiktextract (e9e0a99 and db5a844). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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