===== Lebesgue outer measure =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $p\in \mathbb N$ |

| @#FFBB00: definiendum | @#FFBB00: $\eta^p:\mathcal P(\mathbb R^p)\to \overline{\mathbb R}$ |
| @#FFBB00: definiendum | @#FFBB00: $\eta^p(A):=\mathrm{inf}\{\ \sum_{k=1}^\infty\lambda^p(I_k)\ |\ I\in\mathrm{Sequence}(\mathfrak J^p)\ \land\ A\subset\bigcup_{k=1}^\infty I_k\ \}$ |

==== 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: [[http://en.wikipedia.org/wiki/Lebesgue_measure|Lebesgue measure]]
==== Parents ====
=== Subset of ===
[[Partial function]]
=== Context ===
[[Elementary volume of ℝⁿ]], [[Poset]], [[Sequence union]]