Borel field of events

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.