Average sheet number
= Average sheet number
{title2=$S=A_f(X)/A(Y)$}
For a <holomorphic map> between metric <Riemann surfaces>, the average sheet number is the pulled-back source area divided by the target area. The <area formula> identifies it with the average number of preimages counted with <multiplicity>. The same definition over a target region $D$ gives $S_D=A_f(f^{-1}D)/A(D)$.