Half-open subsets of ℝⁿ

context

$p\in \mathbb N$

definiendum

$\mathfrak J^p\equiv\{\ ]a,b]\ |\ a,b\in\mathbb R^p\ \land\ a\le b\}$

This set is one which generates the $\sigma$ -Algebra $\mathcal B^p$ of Borel subset of $\mathbb R^p$ .

We also write

definiendum

$\mathfrak J\equiv \mathfrak J^1$