Singular probability distributions and fractal properties of sets of real numbers defined by the asymptotic frequencies of their s-adic digits
| dc.creator | Albeverio, S. | |
| dc.creator | Pratsiovytyi, M. | |
| dc.creator | Torbin, G. | |
| dc.date | 2006-05-30 | |
| dc.date.accessioned | 2026-07-07T07:14:39Z | |
| dc.date.available | 2026-07-07T07:14:39Z | |
| dc.description | 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 the asymptotic frequencies in the nonterminating $s-$ adic expansion of $x$, and some do not). It is proven that the set $T_s$ is residual in the topological sense (i.e., it is of the first Baire category) and it is generic in the sense of fractal geometry ($T_s$ is a superfractal set, i.e., its Hausdorff-Besicovitch dimension is equal to~1). A topological and fractal classification of sets of real numbers via analysis of asymptotic frequencies of digits in their s-adic expansions is presented. | |
| dc.description | Published in Ukrainian Mathematical Journal, 57 (2005), no.9, 1361-1370 | |
| dc.identifier | https://arxiv.org/abs/math/0605763 | |
| dc.identifier | http://arxiv.org/abs/math/0605763 | |
| dc.identifier | Ukrainian Mathematical Journal, 57 (2005), no.9, 1361-1370 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112962 | |
| dc.subject | Number Theory | |
| dc.subject | Probability | |
| dc.subject | 11K55; 28A80; 60G30 | |
| dc.title | Singular probability distributions and fractal properties of sets of real numbers defined by the asymptotic frequencies of their s-adic digits | |
| dc.type | text |