Elementary volume of ℝⁿ

context

$p\in \mathbb N$

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

This is also called the Lebesgue pre-measure