Mixed volume

In mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to an ${\displaystyle n}$-tuple of convex bodies in the ${\displaystyle n}$-dimensional space. This number depends on the size and shape of the bodies and on their relative orientation to each other.

Let ${\displaystyle K_{1},K_{2},\dots ,K_{r}}$ be convex bodies in ${\displaystyle \mathbb {R} ^{n}}$ and consider the function

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