Definition:Sigma-Algebra Generated by Collection of Subsets

Definition
Let $X$ be a set.

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

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


 * $\map \MM \GG$
 * $\map {\mathscr M} \GG$

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 $\map \sigma \GG$ always exists, and is unique