Effective Estimate with Self-Similarity for Lebesgue Measure of Some Cantorval

Abstract

We obtain the spectrum and an effective estimate for the Lebesgue measure of the preimages of iterates of Farey and Gauss maps. The intervals and dichotomy between Farey fractions and sequence in the limit of infinite level and uniform distribution of the Stern-Brocot are determined. The structure, topology, separation and measure properties of the self-similar sets and Fractals and interated function systems of bounded distortion are characterize. We examine the asymptotic behavior of the Lebesgue measure of sum-level sets of continued function, self-similarity and nonempty interior. The family of self-affin and self-conformal sets with uniqueness, simultaneous and positive Hausdorff measure are studied. The nultigemetric. Subsum sets of sequences with recovering a purely atomic finite measure and Cantorvals with Lebesgue measure of M-Contorvals of Farey type are established.