Corollary 3.104 . [02NY]

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Corollary 3.104.

Let $f$ be a concave function on $N_{\mathbb{R}}$ such that $\Delta=\operatorname{stab}(f)$ is a lattice polytope of dimension $n$ . Then

-n!\int_{N_{\mathbb{R}}}f{\mathcal{M}}_{M}(f)=(n+1)!\int_{\Delta}f^{\vee}\,\text{\rm d}\operatorname{vol}_{M}+\sum_{F}\langle v_{F},F\rangle n!\int_{F}f^{\vee}\,\text{\rm d}\operatorname{vol}_{M(F)},

where the sum is over the facets $F$ of $\Delta$ .