# Borel field of events

$\sigma$-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.