Let $L$ be a toric line bundle, $s$ a toric section of $L$ and let $\|\cdot\|$ be a toric metric. Denote ${\overline{L}}=(L,\|\cdot\|)$. We define the function $\psi_{{\overline{L}},s}\colon N_{\mathbb{R}}\to\mathbb{R}$ by

(5.15)

$$\psi_{{\overline{L}},s}(u)=\frac{\log\|s(p)\|}{\lambda_{K}}$$

for any $p\in X_{0}^{{\text{\rm an}}}$ with ${\operatorname{val}}_{K}(p)=u$. When the line bundle and the section are clear from the context, we will alternatively denote this function as $\psi_{\|\cdot\|}$.