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 elementary_volume_of_ℝⁿ [2013/09/07 19:39]nikolaj elementary_volume_of_ℝⁿ [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/07 19:39 nikolaj 2013/09/07 19:32 nikolaj 2013/09/06 22:04 external edit2013/09/03 18:56 ben 2013/09/03 18:56 ben 2013/09/03 18:51 ben created 2013/09/07 19:39 nikolaj 2013/09/07 19:32 nikolaj 2013/09/06 22:04 external edit2013/09/03 18:56 ben 2013/09/03 18:56 ben 2013/09/03 18:51 ben created Line 1: Line 1: ===== Elementary volume of ℝⁿ ===== ===== Elementary volume of ℝⁿ ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $p\in \mathbb N$ | + | @#55CCEE: context ​    | @#55CCEE: $p\in \mathbb N$ | - | @#FFBB00: $\mathrm{vol}:​\mathfrak J^p\to \mathrm R$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\mathrm{vol}:​\mathfrak J^p\to \mathrm R$ | - | @#FFBB00: $\mathrm{vol}(]a,​b]):​=\prod_{i=1}^p (b_i-a_i)$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\mathrm{vol}(]a,​b]):​=\prod_{i=1}^p (b_i-a_i)$ | ==== Discussion ==== ==== Discussion ==== This is also called the Lebesgue pre-measure This is also called the Lebesgue pre-measure ==== Parents ==== ==== Parents ==== - === Requirements ​=== + === Context ​=== [[Half-open subsets of ℝⁿ]], [[Finite product of complex numbers]] [[Half-open subsets of ℝⁿ]], [[Finite product of complex numbers]]