ScalingStacks

Theorem 3.97 . [02NU]

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Theorem 3.97.

Let f:Nℝ→ℝf\colon N_{\mathbb{R}}\to\mathbb{R} be a closed concave function, such that D:=stab⁡(f)D:=\operatorname{stab}(f) is a compact convex set with piecewise smooth boundary ∂D\partial D. Then

(3.98) −n!∫Nℝfℳμ(f)=(n+1)!∫Df∨dμ−n!∫∂Df∨λ.-n!\int_{N_{\mathbb{R}}}f{\mathcal{M}}_{\mu}(f)=(n+1)!\int_{D}f^{\vee}\,\text{\rm d}\mu-n!\int_{\partial D}f^{\vee}\lambda.

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