View source for Borel field of events

{{MSC|03E15|28A05}}
[[Category:Descriptive set theory]]
[[Category:Classical measure theory]]
{{TEX|done}}

''[[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]].