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}