\begin{definition}[Definition:Sigma-Algebra Generated by Collection of Subsets/Generator]
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'''.
\end{definition}