Definition:Half-Open Rectangle/Degenerate Case
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Definition
In the case where $a_i > b_i$ for some $i$, the half-open rectangle $\ds \prod_{i \mathop = 1}^n \hointr {a_i} {b_i}$ degenerates to the empty set $\O$.
This is in accordance with the result Cartesian Product is Empty iff Factor is Empty for general Cartesian products.