# Is $\mathscr{C}(K)$ a subspace of every $L^p(K)$, if $K$ is compact?

Considering a function $f\in\mathscr({C}(K),\lvert\lvert \cdot\rvert\rvert_\infty)$, i.e.$$f:K\rightarrow\mathbb{C}$$ everywhere continuous where $K$ is a compact subset of $\mathbb{R}^n$, does $f$ lie in $L^p(K)$ for every $1\le p\le\infty$?