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
▼ Subset structure
▼ Measurable space
▼ Measurable set
▼ Null measurable set
Definition D3802
Subnull set
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $E \subseteq X$ is a D78: Subset of $X$
Then $E$ is a subnull set in $M$ if and only if there exists D1109: Measurable set $F \in \mathcal{F}$ such that
(1) \begin{equation} E \subseteq F \end{equation} (D78: Subset)
(2) \begin{equation} \mu(F) = 0 \end{equation} (D1676: Null measurable set)
Children
▶ D1704: Complete measure
▶ D3804: Set of subnull sets
Results
▶ R3513: Measurable subnull set has measure zero