On the Problem of Convergence of Double Functional Series to $${\mathbf{+}}\boldsymbol{\infty}$$

Abstract

The problem, posed by N.N. Luzin in 1915, on the convergence of trigonometric series to $${+}\infty$$ on the set of positive measure, was solved by S.V. Konyagin in 1988. There naturally arises the question of N.N. Luzin for double trigonometric series. In the present paper the theorem is proved which contains the answer to this problem.