Let $f$ holomorphic, $f:\mathbb{D}\rightarrow\mathbb{D}$.
If $w\in\mathbb{D}$ we denote as $n_f(w)$ the number of zeros of the function $f(z)-w$. If $n_f=1$ almost everywhere in $\mathbb{D}$, show that $f$ is $1-1$ in $\mathbb{D}$.
My thoughts: I know that the set $\{w\in\mathbb{D}:n_f(w)\neq 1\}$ has zero measure which means that this set is measurable but I have no idea on how to proceed with this problem.
Any useful hints or a solution would help me very much as I'm struggling a lot with problems at that level of complex analysis.