I am trying to find the necessary and sufficient condition that, $$\lim\sup(a_nb_n)=\lim\sup(a_n)\lim\sup(b_n)$$ I know equality takes place if one of them converges,but I want to find a condition both necessary and sufficient.Can someone help me on this?
2026-03-28 08:09:38.1774685378
When does equality hold in limsup of product inequality?
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