EXTENSIONS OF TRANSLATION INVARIANT VALUATIONS ON POLYTOPES. Issue 1 (January 2015) - Hinderer, Wolfram; Hug, Daniel; Weil, Wolfgang
Abstract We study translation invariant, real-valued valuations on the class of convex polytopes in Euclidean space and discuss which continuity properties are sufficient for an extension of such valuations to all convex bodies. For this purpose, we introduce flag support measures of convex bodies via a local Steiner formula and derive some of the properties of these measures.