Let $f_{1},\dots,f_{n}$ be concave functions such that $\operatorname{ri}({\operatorname{dom}}(f_{1}))\cap\dots\cap\operatorname{ri}({\operatorname{dom}}(f_{n}))\neq\emptyset$ and $E\subset N_{\mathbb{R}}$ a Borel subset. Then

$${\mathcal{M}}_{M}(f_{1},\dots,f_{n})(E)=\frac{1}{n!}\operatorname{MV}_{M}(\partial f_{1}(E),\dots,\partial f_{n}(E)).$$

If $f_{1},\dots,f_{k}$ are piecewise affine, this formula holds under the weaker hypothesis ${\operatorname{dom}}(f_{1})\cap\dots\cap{\operatorname{dom}}(f_{k})\cap\operatorname{ri}({\operatorname{dom}}(f_{k+1}))\cap\dots\cap\operatorname{ri}({\operatorname{dom}}(f_{n}))\neq\emptyset$.