lebesgue_outer

Lebesgue outer measure

Set

context

$p\in \mathbb N$

definiendum	$\eta^p:\mathcal P(\mathbb R^p)\to \overline{\mathbb R}$
definiendum	$\eta^p(A):=\mathrm{inf}\{\ \sum_{k=1}^\infty\lambda^p(I_k)\ \|\ I\in\mathrm{Sequence}(\mathfrak J^p)\ \land\ A\subset\bigcup_{k=1}^\infty I_k\ \}$

Discussion

The Lebesgue outer aims at measuring subspaces of $\mathcal P(\mathbb R^p)$ as approximated by cubes which themselves are measured via Elementary volume of ℝⁿ.

Reference

Wikipedia: Lebesgue measure

Parents

Subset of

Partial function

Context

Elementary volume of ℝⁿ, Poset, Sequence union