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arXiv · 1607.03604

On fractal faithfulness and fine fractal properties of random variables with independent $\boldsymbol{Q^*}$-digits

Muslem Ibragim·Grygoriy Torbin
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Abstract

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 $q_{0k}$ 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.

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Muslem Ibragim, Grygoriy Torbin. 2016-07-13. On fractal faithfulness and fine fractal properties of random variables with independent $\boldsymbol{Q^*}$-digits. https://doi.org/10.15559/16-vmsta55

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