Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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.

Copyright Heldermann Verlag 2016