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Even valuations on convex bodies


Author: Daniel A. Klain
Journal: Trans. Amer. Math. Soc. 352 (2000), 71-93
MSC (1991): Primary 52A22, 52A38, 52A39, 52B45
DOI: https://doi.org/10.1090/S0002-9947-99-02240-0
Published electronically: May 20, 1999
MathSciNet review: 1487620
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Abstract: 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.


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Additional Information

Daniel A. Klain
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Email: klain@math.gatech.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02240-0
Received by editor(s): June 24, 1996
Received by editor(s) in revised form: September 29, 1997
Published electronically: May 20, 1999
Additional Notes: Research supported in part by NSF grants #DMS 9022140 to MSRI and #DMS 9626688 to the author.
Article copyright: © Copyright 1999 American Mathematical Society

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