  Let $n \in \mathbb{Z}_{\geq 3}$ be given. We prove a
Lebesgue-almost-everywhere pointwise inversion formula for the primitive Siegel
transform in the geometry of numbers; this inversion formula is valid for the
primitive Siegel transform of any even, bounded, and compactly supported Borel
measurable function $f : \mathbb{R}^n \to \mathbb{R}.$
