I'm reading the following proof:
Suppose $\mu(X) < \infty$ and $0 < p< q \leq \infty$. If $q=\infty$ then $L^{q}(\mu) \subseteq L^{p}(\mu)$.
Proof: If $q=\infty$ then $\int_X |f|^{p}d\mu \leq (||f||_{\infty})^{p} \int_X 1d\mu$.
Why we have the above inequality??