## 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