If $f$ is nonnegative and continuous on $[a,b]$, then $\left(\int_a^b f(x)^n \ dx\right)^{1/n}\to\max\limits_{[a,b]} f$
limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$