Singular probability distributions and fractal properties of sets of real numbers defined by the asymptotic frequencies of their s-adic digits

S. Albeverio, M. Pratsiovytyi, G. Torbin

Properties of the set $T_s$ of "particularly non-normal numbers" of the unit interval are studied in details ($T_s$ consists of real numbers $x$, some of whose s-adic digits have t…