Monotone valuations on the space of convex functions

L. Cavallina, A. Colesanti

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


We consider the space Cn of convex functions u defined in R n with values in R [f1g, which are lower semi-continuous and such that limjxj!1 u(x) = 1. We study the valuations defined on C n which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.

Original languageEnglish
Pages (from-to)167-211
Number of pages45
JournalAnalysis and Geometry in Metric Spaces
Issue number1
Publication statusPublished - 2015


  • Convex bodies
  • Convex functions
  • Intrinsic volumes
  • Sub-level sets
  • Valuations


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