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Journal of Convex Analysis 23 (2016), No. 4, 947--980
Copyright Heldermann Verlag 2016

On Measures of Size for Convex Cones

Alberto Seeger
Dept. of Mathematics, University of Avignon, 33 rue Louis Pasteur, 84000 Avignon, France

By using an axiomatic approach we formalize the concept of size index for closed convex cones in the Euclidean space Rn. We review a dozen of size indices disseminated through the literature, commenting on the advantages and disadvantages of each choice.

Keywords: Convex cone, ellipsoidal cone, solid angle, maximal angle, ball-truncated volume, canonical volume, Gaussian width, statistical dimension.

MSC: 28A75, 51M25, 52A20, 52A40

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