ThmDex – An index of mathematical definitions, results, and conjectures.
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Deduction system
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Zermelo-Fraenkel set theory
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Subsigma-algebra
Definition D4467
Sigma-algebra restriction
Formulation 0
Let $X$ be a D11: Set such that
(i) $\mathcal{F} \subseteq \mathcal{P}(X)$ is a D84: Sigma-algebra on $X$
(ii) $E \subseteq X$ is a D78: Subset of $X$
The sigma-algebra restriction of $\mathcal{F}$ on $X$ with respect to $E$ is the D11: Set \begin{equation} \{ F \cap E : F \in \mathcal{F} \} \end{equation}