Measure zero spectrum of a class of Schrödinger operators

We study the measure of the spectrum of a class of one-dimensional discrete Schrödinger operators H_ν,ω with potential ν(ω) generated by any primitive substitutions. It is well known that the spectrum of H_ν,ω is singular continuous. We will give a more exact result that the spectrum of H_ν,ω is a set of Lebesgue measure zero, by removing two hypotheses (the semi-primitive of a certain induced substitution and the existence of square word) from a theorem due to Bovier and Ghez.