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| ===== Lebesgue outer measure ===== | ===== Lebesgue outer measure ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $p\in \mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $p\in \mathbb N$ | |
| - | | @#FFBB00: $\eta^p:\mathcal P(\mathbb R^p)\to \overline{\mathbb R}$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\eta^p:\mathcal P(\mathbb R^p)\to \overline{\mathbb R}$ | |
| - | | @#FFBB00: $\eta^p(A):=\mathrm{inf}\{\ \sum_{k=1}^\infty\lambda^p(I_k)\ |\ I\in\mathrm{Sequence}(\mathfrak J^p)\ \land\ A\subset\bigcup_{k=1}^\infty I_k\ \}$ | | + | | @#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 ==== | ==== 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]]. | 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]]. | ||
| - | ==== Context ==== | + | === Reference === |
| + | Wikipedia: [[http://en.wikipedia.org/wiki/Lebesgue_measure|Lebesgue measure]] | ||
| + | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Partial function]] | [[Partial function]] | ||
| - | === Requirements === | + | === Context === |
| - | [[Elementary volume of ℝⁿ]], [[Poset]] | + | [[Elementary volume of ℝⁿ]], [[Poset]], [[Sequence union]] |
