Distribution of values of a singular non-monotonic function of the Cantor type

Abstract

Let f be a non-monotonic singular function of the Cantor type defined in
terms of quinary representation of the numbers and let $X$ be a random
variable whose digits of its quinary representation are independent of the
random variables. We study a Lebesgue structure of distribution of the
random variable $Y = f(X)$, topological, metric and fractal properties of
its spectrum.