Let $\|\cdot\|$ be a semipositive smooth toric metric on $L^{{\text{\rm an}}}$. Let $c_{1}({\overline{L}})^{n}\land\delta_{X_{\Sigma}}$ be the measure defined by ${\overline{L}}$. Then,

(5.34)

$${\operatorname{val}}_{\ast}(c_{1}({\overline{L}})^{n}\land\delta_{X_{\Sigma}})=n!{\overline{\mathcal{M}}}_{M}(\psi),$$

where ${\operatorname{val}}$ is the map of diagram (5.7). In addition, this measure is uniquely characterized by equation (5.34) and the property of being $\mathbb{S}^{{\text{\rm an}}}$-invariant.