Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions

• Date: 1995
• Main Authors: Pratsiovytyi, M. V., Torbin, H. M., Працьовитий, М. В., Торбін, Г. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1995
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5492
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 lea...