limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
46101
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?
11558
How to show that the limit of compact operators in the operator norm topology is compact
76756
A convergence proof: $\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$
966
Show that $\lim_{n\rightarrow \infty} \sqrt[n]{c_1^n+c_2^n+\ldots+c_m^n} = \max\{c_1,c_2,\ldots,c_m\}$
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
8503
Limit of $L^p$ norm when $p\to0$
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
98367
Limit of $\left(\frac{n^2+2}{2n^2+1}\right)^{n^2}$
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
134787
How to prove $\lim \limits_{n\to\infty}(n+1)\int_{0}^{1}x^nf(x)dx=f(1)$
96848
Prove: $\limsup_{n\to\infty} (a_n)\leq \sup(a_n)_{n=1}^\infty$
47668
Show that $lim_{n \rightarrow \infty}m(O_n)=m(E)$ when $E$ is compact.
91901
Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$
64169
Why isn't $\lim \limits_{x\to\infty}\left(1+\frac{1}{x}\right)^{x}$ equal to $1$?
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
113141
Prove that $\lim_{n \to \infty}\bigg[\int_0^1f(t)^n \text{dt}\bigg]^{1/n}=M$
156141
Limit of $\left(1-\frac{1}{n^2}\right)^n$