  We study Schr\"odinger operators on $\R$ with measures as potentials.
  Choosing a suitable subset of measures we can work with a dynamical system
consisting of measures. We then relate properties of this dynamical system with
spectral properties of the associated operators.
  The constant spectrum in the strictly ergodic case coincides with the union
of the zeros of the Lyapunov exponent and the set of non-uniformities of the
transfer matrices.
  This result enables us to prove Cantor spectra of zero Lebesgue measure for a
large class of operator families, including many operator families generated by
aperiodic subshifts.
