V. Vasylenko

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Articles: 1

On fractal faithfulness and fine fractal properties of random variables with independent $\widetilde{Q}$-symbols

MFAT 32 (2026), no. 2, 181-192

181-192

We prove sufficient conditions for the faithfulness of the family of cylinders generated by $\widetilde{Q}$ -expansions for the Hausdorff-Besicovitch dimension calculation. We also represent the conjecture about necessary and sufficient conditions for such a family of cylinders to be faithful. Based on these new results we study fine fractal properties of random variables with independent $\widetilde{Q}$-digits and prove exact formulae for the calculation of the Hausdorff dimension of the corresponding probability measure.

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