Category:Sigma-Algebras

Let $X$ be a set.
A $\sigma$-algebra $\mathcal R$ over $X$ is a system of subsets of $X$ with the following properties:
 $(SA \, 1)$ $:$ Unit: $\displaystyle X \in \mathcal R$ $(SA \, 2)$ $:$ Closure under Complement: $\displaystyle \forall A \in \mathcal R:$ $\displaystyle \complement_X \left({A}\right) \in \mathcal R$ $(SA \, 3)$ $:$ Closure under Countable Unions: $\displaystyle \forall A_n \in \mathcal R: n = 1, 2, \ldots:$ $\displaystyle \bigcup_{n \mathop = 1}^\infty A_n \in \mathcal R$