sigma-algebra
Definition
A $\sigma$-algebra $\mathcal{A}$ on a set $X$ is a family of subsets of $X$ with the following properties:
($\Sigma_{1}$): $X \in \mathcal{A}$
($\Sigma_{2}$): $A \in \mathcal{A} \Longrightarrow A^{c} \in \mathcal{A}$
($\Sigma_{3}$): $\left. \left( A_{n} \right) \right._{n \in \mathbb{N}} \subseteq \mathcal{A} \Longrightarrow \bigcup(n \in \mathbb{N})A_{n} \in \mathcal{A}$
A set $A \in \mathcal{A}$ is said to be measurable or $\mathcal{A}$-measurable.