2016/06/09 by Muslem Ibragim, Grygoriy Torbin
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics #Computability, Logic, AI Algorithms #Dimension (graph theory) #Discrete mathematics #Fractal #Fractal dimension #Hausdorff dimension #Hausdorff space #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Random variable #Statistics #math.PR
paper · pdf · doi:10.15559/16-vmsta55
published as Modern Stochastics: Theory and Applications 2016, Vol. 3, No. 2, 119-131 · Published at http://dx.doi.org/10.15559/16-VMSTA55 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)
openalex publication_date 2016/06/09 · arxiv created 2016/07/13 · arxiv updated 2016/07/14 · openalex created_date 2016/07/22 · openalex updated_date 2026/08/05
We develop a new technique to prove the faithfulness of the Hausdorff–Besicovitch dimension calculation of the family \varPhi (Q∗ ) of cylinders generated by Q∗ -expansion of real numbers. All known sufficient conditions for the family \varPhi (Q∗ ) to be faithful for the Hausdorff–Besicovitch dimension calculation use different restrictions on entries q0k and q(s-1)k. We show that these restrictions are of purely technical nature and can be removed. Based on these new results, we study fine fractal properties of random variables with independent Q∗ -digits.