Singular Probability Distributions and Fractal Properties of Sets of Real Numbers Defined by the Asymptotic Frequencies of Their s-Adic Digits

• Date: 2005
• Main Authors: Pratsiovytyi, M. V., Torbin, H. M., Працьовитий, М. В., Торбін, Г. М.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3676
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Dedicated to V. S. Korolyuk on occasion of his 80-th birthday Properties of the set $T_s$ of "particularly nonnormal numbers" of the unit interval are studied in details ($T_s$ consists of real numbers $x$, some of whose $s$-adic digits have the asymptotic frequencies in the nonter...