  We show that the measure of the spectrum of Schr\"odinger operator with
potential defined by non-constant function over any minimal aperiodic finite
subshift tends to zero, as the coupling constant tends to infinity. We also
obtained a quantitative upper bound for the measure of the spectrum. This
follows from a result we proved for ergodic Schr\"odinger operators with
finitely valued potentials under two conditions on the recurrence property of
the shift. We also show that one of these conditions is necessary for such
result.
