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EXTENSIONS OF TRANSLATION INVARIANT VALUATIONS ON POLYTOPES

Part of: Polytopes and polyhedra General convexity

Published online by Cambridge University Press:  19 August 2014

Wolfram Hinderer ,
Daniel Hug  and
Wolfgang Weil
Wolfram Hinderer
Affiliation:
Robert-Koch-Str. 196, D-73760 Ostfildern, Germany email wolfram@hinderer-lang.de
Daniel Hug
Affiliation:
Karlsruhe Institute of Technology (KIT), Department of Mathematics, D-76128 Karlsruhe, Germany email daniel.hug@kit.edu
Wolfgang Weil
Affiliation:
Karlsruhe Institute of Technology (KIT), Department of Mathematics, D-76128 Karlsruhe, Germany email wolfgang.weil@kit.edu
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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.

MSC classification

Primary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces) 52A39: Mixed volumes and related topics
Secondary: 52B45: Dissections and valuations (Hilbert's third problem, etc.) 52B11: $n$-dimensional polytopes
Type
Research Article
Information
Mathematika , Volume 61 , Issue 1 , January 2015 , pp. 236 - 258
Copyright
Copyright © University College London 2014 

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