Affine invariant valuations on polytopes
Monika Ludwig, Matthias Reitzner
TL;DR
This paper classifies all affine invariant valuations on convex polytopes in n-dimensional space without assuming continuity, providing a comprehensive understanding of their structure.
Contribution
It offers a complete classification of SL(n) invariant valuations on convex polytopes, including those containing the origin, without continuity constraints.
Findings
Complete classification of SL(n) invariant valuations
Results extend to polytopes containing the origin
No continuity assumptions required
Abstract
A classification of SL invariant valuations on the space of convex polytopes in without any continuity assumptions is established. A corresponding result is obtained on the space of convex polytopes in that contain the origin.
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