In integral geometry (otherwise called geometric probability theory), Hadwiger's theorem states that the space of translation-invariant, finitely additive, not-necessarily-nonnegative set functions defined on finite unions of compact convex sets in R

The theorem was proved by HugoHadwiger, and led to further work on intrinsic volumes.

An account and a proof of Hadwiger's theorem may be found in Introduction to Geometric Probability by Daniel Klain and Gian-Carlo Rota, Cambridge University Press, 1997.

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