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 lebesgue_outer_measure [2013/09/05 00:28]nikolaj lebesgue_outer_measure [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/05 00:36 nikolaj 2013/09/05 00:28 nikolaj 2013/09/04 18:15 nikolaj 2013/09/04 18:10 nikolaj 2013/09/04 18:08 nikolaj 2013/09/04 18:06 nikolaj created Next revision Previous revision 2013/09/05 00:36 nikolaj 2013/09/05 00:28 nikolaj 2013/09/04 18:15 nikolaj 2013/09/04 18:10 nikolaj 2013/09/04 18:08 nikolaj 2013/09/04 18:06 nikolaj created Line 1: Line 1: ===== 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 ==== Line 10: Line 10: === Reference === === Reference === Wikipedia: [[http://​en.wikipedia.org/​wiki/​Lebesgue_measure|Lebesgue measure]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Lebesgue_measure|Lebesgue measure]] - ==== Context ​==== + ==== Parents ​==== === Subset of === === Subset of === [[Partial function]] [[Partial function]] - === Requirements ​=== + === Context ​=== - [[Elementary volume of ℝⁿ]], [[Poset]] + [[Elementary volume of ℝⁿ]], [[Poset]], [[Sequence union]]