(a) State and prove the Mean Value Theorem for harmonic functions.

(b) Let $u \geqslant 0$ be a harmonic function on an open set $\Omega \subset \mathbb{R}^{n}$. Let $B(x, a)=\{y \in$ $\left.\mathbb{R}^{n}:|x-y|<a\right\}$. For any $x \in \Omega$ and for any $r>0$ such that $B(x, 4 r) \subset \Omega$, show that

$$\sup _{\{y \in B(x, r)\}} u(y) \leqslant 3^{n} \inf _{\{y \in B(x, r)\}} u(y) .$$