Given $\gamma \geq 0$ if
$\liminf_{r\rightarrow \infty} \displaystyle\frac{M(f;r)}{r^{\gamma}} = 0$
where $M(f;r) = max \{|f(z)|: |z|=r \}$. Then $f$ is polynom such that his degree are at least $\gamma$.
I can see that $f$ growth is not exponencial so he must be a polynomial, but how can I show that its degree is at least $\gamma$?