MathGloss

A $\sigma$-algebra on the set $X$ is a subset $\mathcal M \subset \mathcal P(X)$ of the power set of $X$ satisfying the following properties:

1. $X \in \mathcal M$;
2. $\mathcal M$ is closed under complementation, i.e. if $A \in \mathcal M$, then $X\setminus A \in \mathcal M$;
3. $\mathcal M$ is closed under countable unions, i.e. if $A_i \in \mathcal M$ for $i \in \mathbb N$, then $\bigcup\limits_{i\in\mathbb N} A_i \in \mathcal M$.

Wikidata ID: Q217357

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