Suppose a situation whereby I know for some bounded collection $a_{m,n}$of real numbers the following:
For any n≥1, $\underset{m→∞}{lim sup}$$a_{m,n}$≤$B_n$and we can choose the $B_n$such that $\underset{n≥1}{sup}$$B_n$< ∞.
Can I conclude that $\underset{m→∞}{lim sup}$($\underset{n≥1}{sup}$$a_{m,n}$) ≤$\underset{n≥1}{sup}$$B_n$?
Counter-examples also appreciated.