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