Topological and metric properties of distributions of random variables represented by the alternating Lüroth series with independent elements

摘要

In the paper we consider the distributions of random variables represented by the alternating Lüroth series (L-expansion). We study Lebesgue structure, topological, metric and fractal properties of these random variables. We prove that random variable with independent L-symbols has a pure discrete, pure absolutely continuous or pure singularly continuous distribution. We describe topological and metric properties of the spectra of distributions of random variables as well as properties of their probability distribution functions.