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lim-inf-A-n-c-limsup-A-n-c-prove-




Question Number 205055 by SANOGO last updated on 06/Mar/24
(lim inf(A_n ))^c  =limsup(A_n ^c )     prove
$$\left({lim}\:{inf}\left({A}_{{n}} \right)\right)^{{c}} \:={limsup}\left({A}_{{n}} ^{{c}} \right)\:\:\:\:\:{prove} \\ $$
Answered by pi314 last updated on 09/Mar/24
What de you mean Withe A_n   A_n ={k;k∈N ∣k≥n} ....?
$${What}\:{de}\:{you}\:{mean}\:{Withe}\:{A}_{{n}} \\ $$$${A}_{{n}} =\left\{{k};{k}\in\mathbb{N}\:\mid{k}\geqslant{n}\right\}\:….? \\ $$

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