Elementary volume of ℝⁿ

Set

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

Discussion

This is also called the Lebesgue pre-measure