Difference between revisions of "Borel field of events"
From Encyclopedia of Mathematics
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''[[Field of sets|$\sigma$-field]], Borel algebra, [[Algebra of sets|$\sigma$-algebra of events]]'' | ''[[Field of sets|$\sigma$-field]], Borel algebra, [[Algebra of sets|$\sigma$-algebra of events]]'' | ||
A class $\mathcal{B}$ of subsets (events) of a non-empty set $\Omega$ (the space of elementary events) which is a [[Algebra of sets|$\sigma$-algebra]] | A class $\mathcal{B}$ of subsets (events) of a non-empty set $\Omega$ (the space of elementary events) which is a [[Algebra of sets|$\sigma$-algebra]] | ||
(alternatively called [[Field of sets|$\sigma$-field]] or Boolean $\sigma$-algebra). The Borel field of events generated by $M$ is the smallest $\sigma$-algebra containing the family $M$ of events (i.e. of subsets of $\Omega$). See also [[Borel field of sets]]. | (alternatively called [[Field of sets|$\sigma$-field]] or Boolean $\sigma$-algebra). The Borel field of events generated by $M$ is the smallest $\sigma$-algebra containing the family $M$ of events (i.e. of subsets of $\Omega$). See also [[Borel field of sets]]. | ||
Latest revision as of 13:02, 6 December 2012
2020 Mathematics Subject Classification: Primary: 03E15 Secondary: 28A05 [MSN][ZBL]
$\sigma$-field, Borel algebra, $\sigma$-algebra of events
A class $\mathcal{B}$ of subsets (events) of a non-empty set $\Omega$ (the space of elementary events) which is a $\sigma$-algebra (alternatively called $\sigma$-field or Boolean $\sigma$-algebra). The Borel field of events generated by $M$ is the smallest $\sigma$-algebra containing the family $M$ of events (i.e. of subsets of $\Omega$). See also Borel field of sets.
How to Cite This Entry:
Borel field of events. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Borel_field_of_events&oldid=29099
Borel field of events. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Borel_field_of_events&oldid=29099
This article was adapted from an original article by V.V. Sazonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article