The following lemma is true (see DeGiorgi oscillation lemma)
Let $u$ be a subsolution of $$\mathrm{div}(A(x)\nabla u) = 0,$$ where $A$ is bounded, measurable and uniformly elliptic ($C^{-1}\mathrm{Id} \le A(x) \le C \mathrm{Id}$) in $B(0,1)$ such that $u \le 1$ and $|\{ u \le 0\}| =a>0$. Then $$\sup_{B_{1/2}}u \le \mu(a) < 1.$$
How does this lemma imply the following? $$\sup_{B_{r/2}} u \le \mu \sup_{B_r} u$$ for $r<1$?
