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

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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.


Sources


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