ScalingStacks

Proposition 3.94 . [02NP]

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Proposition 3.94.

Let CC be an open convex set in NℝN_{\mathbb{R}} and fβˆˆπ’ž2​(C)f\in{\mathcal{C}}^{2}(C) a concave function. Then

ℳμ​(f)=(βˆ’1)n​det(Hess⁑(f))​d​u1βˆ§β‹―βˆ§d​un,{\mathcal{M}}_{\mu}(f)=(-1)^{n}\det(\operatorname{Hess}(f))\,\text{\rm d}u_{1}\land\dots\land\,\text{\rm d}u_{n},

where the Hessian matrix is calculated with respect to the coordinates (u1,…,un)(u_{1},\dots,u_{n}).

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