Property about positive harmonic functions

Question

Let $U$ be a region and $K$ a compact subset of $U$. Fix a $z_{0} \in U$. Why does there exist positive real numbers $\alpha$ and $\beta$ such that $$\alpha u(z_{0}) \leq u(z) \leq \beta u(z_{0})$$ for every positive harmonic function $u$ in $U$ and for all $z \in K$?