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)	$\mathcal{P}_{\text{elementary}}(\mathbb{R}^N)$ is the D3761: Set of elementary sets in $\mathbb{R}^N$
(iii)	$m$ is the D3760: Elementary measure in $\mathbb{R}^N$

The Jordan outer measure in $\mathbb{R}^N$ is the D4361: Unsigned basic function \begin{equation} \mathcal{P}_{\text{bounded}}(\mathbb{R}^N) \to [0, \infty], \quad B \mapsto \inf_{E \in \mathcal{P}_{\text{elementary}}(\mathbb{R}^N) : B \subseteq E} m(E) \end{equation}