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Definition D3763
Jordan outer measure

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 $$\mathcal{P}_{\text{bounded}}(\mathbb{R}^N) \to [0, \infty], \quad B \mapsto \inf_{E \in \mathcal{P}_{\text{elementary}}(\mathbb{R}^N) : B \subseteq E} m(E)$$
Children
 ▶ Set of Jordan measurable sets