ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Boolean algebra
Sigma-algebra
Definition D470
Subsigma-algebra
Formulation 0
Let $X$ be a D11: Set such that
(i) $\mathcal{F} \subseteq \mathcal{P}(X)$ is a D84: Sigma-algebra on $X$
A D11: Set $\mathcal{G}$ is a subsigma-algebra of $\mathcal{F}$ on $X$ if and only if
(1) \begin{equation} \mathcal{G} \subseteq \mathcal{F} \end{equation}
(2) $\mathcal{G}$ is a D84: Sigma-algebra on $X$
Children
D3344: Set of subsigma-algebras
D4467: Sigma-algebra restriction