Difference between revisions of "Borel field of events"
From Encyclopedia of Mathematics
(Importing text file) |
m |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | + | {{MSC|03E15|28A05}} | |
| + | [[Category:Descriptive set theory]] | ||
| + | [[Category:Classical measure theory]] | ||
| + | {{TEX|done}} | ||
| − | A class | + | ''[[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]] | ||
| + | (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=18357
Borel field of events. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Borel_field_of_events&oldid=18357
This article was adapted from an original article by V.V. Sazonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article