$L^{\infty}(\mu)$ is $C(K)$ for some compact Hausdorff space $K$ when $\mu$ is sigma-finite

Question

I am looking for a proof (or at least an article or book in which it is stated) that for measure space $(X, A, \mu)$, where $\mu$ is sigma-finite, there exists compact Hausdorff space K such that $L^{\infty}(\mu)$ is isometrically isomorphic to $C(K)$. I also know that such $K$ should be extremally disconnected. Do you know where I can find it?