Про розподіл значень однієї сингулярної функції, пов'язаної з зображенням чисел рядами Люрота

Abstract

In the article we study the distribution of the random variable $Y = F (X)$, where $X$ --- is evenly distributed on $[0; 1]$ random variable, $F$ --- distribution function, the digits of which are positive by the Lurot's rows are independent and equally distributed random variables. The problem of the Lebesgue structure of the distribution $Y$ is solved, the criterion of discreteness (and continuity) of the distribution $Y$ is proved, the conditions under which the distribution is not pure are found.