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elementary_volume_of_ℝⁿ [2013/09/06 22:04] 127.0.0.1 external edit |
elementary_volume_of_ℝⁿ [2014/03/21 11:11] (current) |
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| ===== 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 series]] | + | [[Half-open subsets of ℝⁿ]], [[Finite product of complex numbers]] |
