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## Lebesgue measure

### Definition

 $p\in \mathbb N$
 $\lambda^p\equiv\eta^p|_{\mathfrak{L}^p}$

### Discussion

$\lambda^p:\mathfrak{L}^p\to \overline{\mathbb{R}}$ is the restriction of Lebesgue outer measure to a domain which contains only actually measurable sets.