Zero measure spectrum for the almost Mathieu operator

We study the almost Mathieu operator: (H_{α, λ, θ}u)(n)=u(n+1)+u(n-1)+λ cos (2παn+θ)u(n), on l²(Z), and show that for all λ,θ, and (Lebesgue) a.e. α, the Lebesgue measure of its spectrum is precisely |4-2|λ{norm of matrix}. In particular, for |λ|=2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational α's (and |λ|=2) we show that the Hausdorff dimension of the spectrum is smaller than or equal to 1/2.