Is $\lim_{n \to \infty} \lim_{l \to \infty} \ a_{n,l} = \lim_{l \to \infty} \lim_{n \to \infty} \ a_{n,l}\;$? Is $\lim_{n \to \infty} \lim_{l \to \infty} \ a_{n,l} = \lim_{l \to \infty} \lim_{n \to \infty} \ a_{n,l}\;$?
What happens if I replace limits with lim sups?
Thanks!

For positive integers $m$ and $n$, let $(a_{m,n})$ be the sequence with $m$ $0$'s followed by all $1$'s. Then $\lim_{m\to\infty}\lim_{n\to\infty}=1$ but $\lim_{n\to\infty}\lim_{m\to\infty}=0$.
