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Elementary volume of ℝⁿ

Definition

 $p\in \mathbb N$
 $\mathrm{vol}:\mathfrak J^p\to \mathrm R$ $\mathrm{vol}(]a,b]):=\prod_{i=1}^p (b_i-a_i)$

Discussion

This is also called the Lebesgue pre-measure