ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F3267 on D3483: Atomic measurable set
F3267
Formulation 0
Let $M = (X, \mathcal{F})$ be a D1108: Measurable space.
A D1109: Measurable set $E \in \mathcal{F}$ is an atomic measurable set in $M$ if and only if
(1) \begin{equation} E \neq \emptyset \end{equation}
(2) \begin{equation} \forall \, F \in \mathcal{F} \left( F \subseteq E \quad \implies \quad F = \emptyset \text{ or } F = E \right) \end{equation}