Convergence and Integrability of Series with Monotone Decreasing Coefficients by Chrestenson-Levy Systems

In this paper we consider problems of convergence and integrability of series with monotone decreasing coefficients by Chrestenson - Levy systems. In particular we generalize some results, known for classical Walsh systems. Interest in questions arises due to a rapidly developed greedy algorithm in recent years, where in particular the important role played a representation of functions by series with monotone coefficients.