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
▼ Bottom sigma-algebra
Definition D963
Empty sigma-algebra
Formulation 0
Let $\emptyset$ be the D13: Empty set.
A D11: Set $\mathcal{F} \subseteq \mathcal{P}(\emptyset)$ is an empty sigma-algebra on $\emptyset$ if and only if \begin{equation} \mathcal{F} = \{ \emptyset \} \end{equation}