  Regular model sets, describing the point positions of ideal
quasicrystallographic tilings, are mathematical models of quasicrystals. An
important result in mathematical diffraction theory of regular model sets,
which are defined on locally compact Abelian groups, is the pure pointedness of
the diffraction spectrum. We derive an extension of this result, valid for
dense point sets in Euclidean space, which is motivated by the study of
quasicrystallographic random tilings.
