Definition:Sigma-Algebra Generated by Collection of Subsets

Definition
Let $X$ be a set.

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

Also denoted as
Variations of the letter "$M$" can be seen for the $\sigma$-algebra generated by $\mathcal G$:


 * $\map {\mathcal M} {\mathcal G}$
 * $\map {\mathscr M} {\mathcal G}$

Also see

 * Equivalence of Definitions of Sigma-Algebra Generated by Collection of Subsets


 * Existence and Uniqueness of Sigma-Algebra Generated by Collection of Subsets, where it is shown that $\map \sigma {\mathcal G}$ always exists, and is unique