Double trigonometric series with lacunary constant sign coefficients

The article presents an analogue of Sidon's theorem for series of the form
$$ \sum \limits_{k = 1}^\infty\sum\limits_{n=0}^\infty a_{k,n} \cos {m_k x}\cos{ny}, $$
where the coefficients $a_{k,n}$ have a constant sign for any fixed $k$.