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Theory of Probability and Mathematical Statistics



A probabilistic approach to studies of DP-transformations and faithfullness of covering systems to evaluate the Hausdorff-Besicovitch dimension

M. H. Ibragim, G. M. Torbin

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Abstract: This paper is devoted to the development of a probabilistic approach to transformations preserving the Hausdorff-Besicovitch dimension. New relations between fractal faithfulness of fine covering systems and DP-properties of related probability distribution functions are found. Necessary and sufficient conditions for the probability distribution functions of random variables with independent $ Q^*$-symbols to be DP-functions are obtained.

Keywords: Singularly continuous probability distributions, Q∗-representations, DP-transformations, faithful covering systems, Hausdorff-Besicovitch dimension of sets, Hausdorff dimension of probability measures

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