Weighted inverse multiplicity
= Weighted inverse multiplicity
{title2=$m_a(w)=\sum_{a(v)=w}|\det Da(v)|^{-1}$}
For a smooth <local diffeomorphism> $a:\mathbb R^d\to\mathbb R^d$, each inverse branch contributes an inverse <Jacobian determinant> in the <area formula>. Their sum is the weighted inverse multiplicity. A lower determinant bound controls each branch separately, not the number of branches. Bounded weighted inverse multiplicity is sufficient for <dispersion with a nonlinear velocity map>.