EXTENSIONS OF TRANSLATION INVARIANT VALUATIONS ON POLYTOPES. Issue 1 (19th August 2014) - 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.