  We prove that a primitive substitution Delone set, which is pure point
diffractive, is a Meyer set. This answers a question of J. C. Lagarias. We also
show that for primitive substitution Delone sets, being a Meyer set is
equivalent to having a relatively dense set of Bragg peaks. The proof is based
on tiling dynamical systems and the connection between the diffraction and
dynamical spectra.
