ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Binary endorelation
Preordering relation
Partial ordering relation
Partially ordered set
Set of intervals
Real N-interval
Set of euclidean real intervals
Elementary euclidean real set
Elementary euclidean real partition
Elementary euclidean real volume
Elementary euclidean real volume function
Elementary measure
Jordan outer measure
Set of Jordan measurable sets
Definition D3766
Jordan measure
Formulation 0
Let $\mathbb{R}^N$ be a D5630: Set of euclidean real numbers such that
(i) $J^+$ is the D3763: Jordan outer measure in $\mathbb{R}^N$
(ii) $\mathcal{J} = \mathcal{J}(\mathbb{R}^N)$ is the D3765: Set of Jordan measurable sets in $\mathbb{R}^N$
The Jordan measure in $\mathbb{R}^N$ is the D4361: Unsigned basic function \begin{equation} \mathcal{J} \to [0, \infty], \quad E \mapsto J^+(E) \end{equation}