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 D195
Discrete sigma-algebra
Formulation 0
Let $X$ be a D11: Set.
Let $\mathcal{P}(X)$ be the D80: Power set of $X$.
A D11: Set $\mathcal{F} \subseteq \mathcal{P}(X)$ is the discrete sigma-algebra on $X$ if and only if \begin{equation} \mathcal{F} = \mathcal{P}(X) \end{equation}
Children
▶ D1700: Discrete measurable space