Lebesgue measure and Hausdorff dimension of special sets of real numbers from (0,1)

Abstract

We estimate the Hausdorff dimension and the Lebesgue measure of sets of continued fractions of the type a=[a1,a2,…] where an belongs to a set Sn⊂ℕ for every n∈ℕ. An upper bound for the Hausdorff dimension of the set of numbers with continued fraction expansions which fulfill some properties of asymptotic densities is also included.