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

Definition
Let $X$ be a set.

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

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

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

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