Definition 3.109 . [02P4]

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Definition 3.109.

The mixed volume of a family of compact convex sets $Q_{1},\dots,Q_{n}$ of $M_{\mathbb{R}}$ is defined as

(3.110)

\operatorname{MV}_{M}(Q_{1},\dots,Q_{n})=\sum_{j=1}^{n}(-1)^{n-j}\sum_{1\leq i_{1}<\cdots<i_{j}\leq n}\operatorname{vol}_{M}(Q_{i_{1}}+\cdots+Q_{i_{j}})