Fractal properties of random variables with independent 𝑄_{∞}-symbols

Nikiforov, R.; Torbin, G.

doi:10.1090/S0094-9000-2013-00896-5

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

Authors: R. O. Nikiforov and G. M. Torbin
Translated by: S. V. Kvasko
Journal: Theor. Probability and Math. Statist. 86 (2013), 169-182
MSC (2010): Primary 60G30, 11K55, 28A80
DOI: https://doi.org/10.1090/S0094-9000-2013-00896-5
Published electronically: August 20, 2013
MathSciNet review: 2986457
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Abstract | References | Similar Articles | Additional Information

Abstract: We study an equivalent definition of the Hausdorff-Besicovitch dimension in terms of a system $\Phi (Q_\infty )$ of cylinders of the $Q_\infty$-expansion. Sufficient conditions for the system $\Phi (Q_\infty )$ to be faithful for the evaluation of the Hausdorff–Besicovitch dimension in the unit interval are found; fine fractal properties of probability measures with independent $Q_\infty$-digits are investigated (we do not assume that the $Q_\infty$-digits are identically distributed).

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