Superfractality of the set of numbers having no frequency of<em class="a-plus-plus">n</em>-adic digits, and fractal probability distributions

Abstract

We study the fractal properties (we find the Hausdorff-Bezikovich dimension and Hausdorff measure) of the spectrum of a random variable with independentn-adic (n≥2,n ∃N digits, the infinite set of which is fixed. We prove that the set of numbers of the segment [0, 1] that have no frequency of at least onen-adic digit is superfractal.