Definition:Closed Rectangle/Degenerate Case

Definition

In the case where $a_i > b_i$ for some $i$, the closed rectangle $\ds \prod_{i \mathop = 1}^n \closedint {a_i} {b_i}$ is taken to be the empty set $\O$.

This is in accordance with the result Cartesian Product is Empty iff Factor is Empty for general Cartesian products.