Minkowski's fundamental theorem and the Minkowski-Hlawka theorem play basic complementary roles in the Geometry of Numbers. Blichfeldt showed essentially that Minkowski's fundamental theorem was a simple consequence of a more general theorem, in which the convex body was replaced by any measurable set and the lattice was replaced by a discrete set of points having a definite asymptotic density. Hlawka himself showed that the Minkowski-Hlawka theorem could be proved in a slightly modified form, when the star body was replaced by any measurable set, but he did not replace the lattice by a more general set of points.