Even valuations on convex bodies,
Transactions of the American Mathematical Society,
352 (2000), 71-93.
The notion of even valuation is introduced as a natural
generalization of volume on compact convex subsets of Euclidean space.
A recent characterization theorem for volume leads in turn to a
connection between even valuations on compact convex sets and continuous
functions on Grassmannians. This connection can be described in part
using generating distributions for symmetric compact convex sets. We
also explore some consequences of these characterization results in
convex and integral geometry.
A pdf file for this paper is available
here.
This paper can be viewed as a sequel to my paper on
Hadwiger's characterization theorem.
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