On packing dimension preservation by distribution functions of random variables with independent \(\tilde{Q}\)-digits

DOI10.15559/15-VMSTA44zbMath1349.28007arXiv1601.01135MaRDI QIDQ340797

Oleksandr Slutskyi

Publication date: 15 November 2016

Published in: Modern Stochastics. Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01135

zbMATH Keywords

\(\tilde{Q} \)-expansion of real numbersfaithfulness of fine packing system for packing dimension calculationHausdorff-Besicovitch dimension of a setpacking dimension of a setpacking-dimension-preserving transformations

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Cites Work

• A class of probability distribution functions preserving the packing dimension
• Fractal properties of singular probability distributions with independent \(Q^{\ast}\)-digits
• Transformations preserving the Hausdorff-Besicovitch dimension
• Fractal properties of random variables with independent $Q_{\infty }$-symbols
• Two definitions of fractional dimension
• Fractal probability distributions and transformations preserving the HausdorffBesicovitch dimension
• On the Hausdorff dimension faithfulness and the Cantor series expansion
• Billingsley’s packing dimension
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