Definition:Sigma-Algebra Generated by Collection of Subsets/Generator

Definition
Let $X$ be a set.

Let $\mathcal G \subseteq \powerset X$ be a collection of subsets of $X$.

Let $\map \sigma {\mathcal G}$ be the $\sigma$-algebra generated by $\mathcal G$.

One says that $\mathcal G$ is a generator for $\map \sigma {\mathcal G}$.

Also, elements $G$ of $\mathcal G$ may be called generators.