  We study discrete quasiperiodic Schr\"odinger operators on $\ell^2(\zee)$
with potentials defined by $\gamma$-H\"older functions. We prove a general
statement that for $\gamma >1/2$ and under the condition of positive Lyapunov
exponents, measure of the spectrum at irrational frequencies is the limit of
measures of spectra of periodic approximants. An important ingredient in our
analysis is a general result on uniformity of the upper Lyapunov exponent of
strictly ergodic cocycles.
