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

Continuity of the measure of the spectrum for quasiperiodic Schrodinger operators with rough potentials