Even valuations on convex bodies
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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.References
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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
- 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.
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1487620