Fractal properties of random variables with independent $Q_{\infty }$-symbols

DOI10.1090/S0094-9000-2013-00896-5zbMath1300.60055OpenAlexW1976219484MaRDI QIDQ2922897

Grygoriy Torbin, Roman Nikiforov

Publication date: 15 October 2014

Published in: Theory of Probability and Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0094-9000-2013-00896-5

zbMATH Keywords

Hausdorff-Besicovitch dimension of a setHausdorff dimension of a measuresingularly continuous probability distributions\(Q_\infty\)-expansionsfaithful systems of coverings

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Continuity and singularity of induced measures (60G30)

Related Items (8)

On new fractal phenomena connected with infinite linear IFS ⋮ On packing dimension preservation by distribution functions of random variables with independent \(\tilde{Q}\)-digits ⋮ On fractal faithfulness and fine fractal properties of random variables with independent \(Q^*\)-digits ⋮ On spectra of probability measures generated by GLS-expansions ⋮ On singularity of distribution of random variables with independent symbols of Oppenheim expansions ⋮ On the $G$-isomorphism of probability and dimensional theories of representations of real numbers and fractal faithfulness of systems of coverings ⋮ On fractal properties of non-normal numbers with respect to Rényi \(f\)-expansions generated by piecewise linear functions ⋮ A probabilistic approach to studies of DP-transformations and faithfullness of covering systems to evaluate the Hausdorff–Besicovitch dimension

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