Level sets of asymptotic mean of digits function for 4 -adic representation of real number

Pratsiovytyi, M. V.; Klymchuk, S. O.; Makarchuk, O. P.

dc.contributor.author	Pratsiovytyi, M. V.
dc.contributor.author	Klymchuk, S. O.
dc.contributor.author	Makarchuk, O. P.
dc.date.accessioned	2024-11-11T08:51:11Z
dc.date.available	2024-11-11T08:51:11Z
dc.date.issued	2016
dc.identifier.citation	Pratsiovytyi, M. V. Level sets of asymptotic mean of digits function for 4 -adic representation of real number / M. V. Pratsiovytyi, S. O. Klymchuk, O. P. Makarchuk // Methods of Functional Analysis and Topology : Quarterly journal. – 2016. - Vol. 22, № 2. - pp. 184-196.	uk
dc.identifier.uri	http://enpuir.npu.edu.ua/handle/123456789/46666
dc.description.abstract	We study topological, metric and fractal properties of the level sets Sθ = {x : r(x) = θ} of the function r of asymptotic mean of digits of a number x ∈ [0; 1] in its 4-adic representation, r(x) = lim n→∞ 1 n Xn i=1 αi(x) if the asymptotic frequency νj (x) of at least one digit does not exist, were νj (x) = lim n→∞ n −1#{k : αk(x) = j, k 6 n}, j = 0, 1, 2, 3.	uk
dc.description.abstract		uk
dc.language.iso	en	uk
dc.subject	s-Adic representation	uk
dc.subject	asymptotic mean of digits function	uk
dc.subject	level sets	uk
dc.subject	frequency of digits	uk
dc.subject	Besicovitch–Eggleston sets	uk
dc.subject	Hausdorff–Besicovitch dimension	uk
dc.title	Level sets of asymptotic mean of digits function for 4 -adic representation of real number	uk
dc.type	Article	uk