\begin{definition}[Definition:Sigma-Algebra Generated by Collection of Subsets/Definition 2]
Let $X$ be a set.
Let $\GG \subseteq \powerset X$ be a collection of subsets of $X$.
The '''$\sigma$-algebra generated by $\GG$''', $\map \sigma \GG$, is the intersection of all $\sigma$-algebras on $X$ that contain $\GG$.
\end{definition}