In 1964 Šalát presented a notion of asymptotic density of single dimensional subseries. Using this notion he presented a series of theorems similar to the following. If ${d_n}$ be a decreasing sequence such that $\liminf_n nd_n>0$ and let the subseries $(x)=\sum_{k=1}^{\infty}\epsilon_k(x)d_k$ of the series $\sum_{k=1}^{\infty}d_k$ be convergent, then $p(x)=\lim_n\frac{p(n,x)}{n}=0$. Following Šalát's patten, we present a notion of double subseries and a natural variation of Šalát's theorem.