ScalingStacks

Notice $\text{Int}(\Delta_{J})\subset\Delta_{\mathcal{X}}$ inherits a natural integral affine structures. Since the restriction of $\phi_{0}$ is convex on these faces by Prop. 5.2, its real MA measure makes sense, and by Prop. 5.4 it satisfies the real MA equation on $\text{Int}(\Delta_{J})$

$$\text{MA}_{\mathbb{R}}(\phi_{0})=\frac{(L^{n})}{n!}d\mu_{0}.$$

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