Definition of lim sup
43197
Showing that two definitions of $\limsup$ are equivalent
16718
Doubt about step of the proof that $\limsup\limits_{n\to\infty}\left|\sum\limits_{\ell=1}^mz^n_\ell\right|^{1/n}=\max\limits_{1\le\ell\le m}|z_\ell|$
147941
comparing sup and inf of two sets
27482
How to show $-\sup(-A)=\inf(A)$?
125011
Show lim sup (an) = lim inf (an) for increasing for increasing sequence of subsets.
68913
Proving that $1_{\limsup A_n}=\limsup1_{A_n}$.
62377
max and min versus sup and inf
43168
Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right) $ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$
22804
Interpretation of limsup-liminf of sets
45988
limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
29849
How can I show that $\sup(AB)\geq\sup A\sup B$ for $A,B\subset\mathbb{R}$ where $A\cup B$ is positive and bounded?
33030
Proof that $\inf A = -\sup(-A)$
130270
Is there a concept of soft limit?
21070
Lim inf with norm and weak convergence
46775
If $\sigma_n=\frac{s_1+s_2+\cdots+s_n}{n}$ then $\operatorname{{lim sup}}\sigma_n \leq \operatorname{lim sup} s_n$
87918
liminf and limsup with characteristic (indicator) function