# 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

- 2005: René L. Schilling:
*Measures, Integrals and Martingales*... (previous) ... (next): $3.4 \ \text{(ii)}$

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- 1984: Gerald B. Folland:
*Real Analysis: Modern Techniques and their Applications*: $\S 1.2$