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
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