Valency theorem
= Valency theorem
For a nonconstant analytic map $f:R\to S$ between compact connected Riemann surfaces, there is an integer $\deg f$ such that for every $w\in S$,
$$
\sum_{z\in f^{-1}(w)}m_f(z)=\deg f.
$$
The degree counts sheets with multiplicity of the associated <branched covering>.