Equation 5.16.2D4BCC2E76B62

\begin{equation} \nu (\varphi ,x)\coloneqq \sup \left\{ \gamma \in \mathbb {R}_{\geq 0}: \varphi (F^{-1}(y))\leq \gamma \log |y-F(x)|^2+\mathcal{O}(1)\textup{ as }y\to F(x) \right\} . \end{equation}