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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 31, 2015

Monotone Valuations on the Space of Convex Functions

  • L. Cavallina and A. Colesanti


We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn 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.


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Received: 2015-3-28
Accepted: 2015-6-16
Published Online: 2015-7-31

© 2015 L. Cavallina and A. Colesanti

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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