# Borel field of events

From Encyclopedia of Mathematics

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

This article was adapted from an original article by V.V. Sazonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article