Valuation (geometry) (original) (raw)

In geometry, a valuation is a finitely additive function on a collection of admissible subsets of a fixed set with values in an abelian semigroup. For example, the Lebesgue measure is a valuation on finite unions of convex bodies (that is, non-empty compact convex sets) of Euclidean space Other examples of valuations on finite unions of convex bodies are the surface area, the mean width, and the Euler characteristic.