Abstract

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

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Keywords

  • Convex cone
  • ellipsoidal cone
  • solid angle
  • maximal angle
  • ball-truncated volume
  • canonical volume
  • Gaussian width
  • statistical dimension

Mathematics Subject Classification

28A75, 51M25, 52A20, 52A40

Suggested citation

A. Seeger. “On Measures of Size for Convex Cones.” Journal of Convex Analysis 23 (2016), No. 4, 947–980. https://doi.org/10.68381/jca23036

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Published by Heldermann Verlag, 2016. Rights now held by Banach Press.