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

Muslem Ibragim, Grygoriy Torbin

We develop a new technique to prove the faithfulness of the Hausdorff--Besicovitch dimension calculation of the family $\Phi (Q^{\ast })$ of cylinders generated by $Q^{\ast }$-expansion of r…