 Lp inclusion on a finite measure space

On a finite measure space, $L^q\subseteq L^p$ for $0<p<q\le \infty$. For $1\le p<q<\infty$, Hölder's inequality giveswith the same formula interpreted as $\Vert f{\Vert }_p\le \mu (X{)}^{1/p}\Vert f{\Vert }_{\infty }$ when $q=\infty$.