Let $D_{\Psi_{i}}$, $i=1,\dots,n$, be $\mathbb{T}$-Cartier divisors on $X_{\Sigma}$ generated by their global sections. Then

(4.38)

$$(D_{\Psi_{1}}\cdot\dots\cdot D_{\Psi_{n}})=\operatorname{MV}_{M}(\Delta_{\Psi_{1}},\dots,\Delta_{\Psi_{n}}).$$

where $\operatorname{MV}_{M}$ denotes the mixed volume function associated to the Haar measure $\operatorname{vol}_{M}$ on $M_{\mathbb{R}}$ (Definition 3.109). In particular, for a $\mathbb{T}$-Cartier divisor $D_{\Psi}$ generated by its global sections,

(4.39)

$$\deg_{D_{\Psi}}(X_{\Sigma})=(D_{\Psi}^{n})=n!\operatorname{vol}_{M}(\Delta_{\Psi}).$$