Level sets of asymptotic mean of digits function for 4-adic representation of real number - Pratsiovytyi, M. V.; Klymchuk, S. O.; Makarchuk, O. P. (Methods of Functional Analysis and Topology, 2016)
We study topological, metric and fractal properties of the level sets S_θ={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)=_n→∞1n^n_i=1α_i(x) if the asymptotic frequency u_j(x) of at least one digit does not exist, were u_j(x)=_n→∞n^-1#{k: α_k(x)=j, kn}, \:\: j=0,1,2,3.