See σ-algebra in All languages combined, or Wiktionary
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": "2013, Alexandr A. Borovkov, Probability Theory, Springer, page 15",
"text": "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).",
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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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