I have two questions about Eremenko's paper On the iteration of entire functions
On the second page, it says "The family $\{f^n\}=\{\underbrace{f\circ f\circ\ldots\circ f}_{n}:n\in \mathbb{N}\}$ is not normal in $V$, hence there exists a pre-image $z^*\in V$ of one of the points $z_1,z_2$". Why does there exist such a pre-image?
Also, at the bottom of that page, it mentions a set $E$ which they call an exceptional set that depends on the function $f$ and $\alpha$ that has finite logarithmic measure. What does this mean?
If a family of entire functions omits two points $\{z_1,z_2\}$, then it's a normal family, by a theorem of Montel.
Finite logarithmic measure is explained right there at the bottom of page 2, following "i.e.". It means a set $E$ such that $\int_E dt/t<\infty$.