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

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

We study topological, metric and fractal properties of the level sets $$S_{\theta }=\{x:r(x)=\theta \}$$ of the function $r$ of asymptotic mean of digits of a number $x\in [0;1]$ in its $4$-adic…