▾ 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
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}
Child definitions
» D1700: Discrete measurable space