Given a double sequence $(a_{n,m})_{n,m \in \mathbb{N}}$ with $0 \leq a_{n,m} \leq C$ for some constant $C > 0$, and knowing that $\liminf_{n \to \infty} a_{n,m} = 0$ for any fixed $m$, does it follow that $$ \liminf_{n \to \infty} \left( \limsup_{m \to \infty} a_{n,m} \right) = 0? $$ I am looking for a proof or counterexample of this statement.
2026-03-09 05:46:30.1773035190
Lim Inf and Lim Sup of Double Sequences
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