(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 $\mathbb{R}^N$ |

**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}