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
Formulation 0
Let $\mathbb{R}^N$ be a D5630: Set of euclidean real numbers such that
(i) $\mathcal{P}_{\text{bounded}}(\mathbb{R}^N)$ is the D3756: Set of bounded euclidean real sets in $\mathbb{R}^N$
(ii) $J^+$ is the D3763: Jordan outer measure in $\mathbb{R}^N$
(iii) $J^-$ is the D3762: Jordan inner measure in $\mathbb{R}^N$
The set of Jordan measurable sets in $\mathbb{R}^N$ is the D11: Set \begin{equation} \left\{ E \in \mathcal{P}_{\text{bounded}}(\mathbb{R}^N) : J^-(E) = J^+(E) \right\} \end{equation}
Child definitions
» D3766: Jordan measure