Lebesgue measure

Set

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

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.

Reference

Wikipedia: Lebesgue measure