Conditions for passing limit inside a series

Question

Consider a succession $\{f_{n,k}\}_{n,k}$ s.t. for any fixed $k$, $\lim_{n\rightarrow\infty}f_{n,k}=g_k$. Which are the conditions s.t. \begin{equation} \lim_{n\rightarrow\infty}\sum_{k}f_{n,k}=\sum_{k}g_k \; \;? \end{equation}