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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

IMPACT FACTOR 2018: 0.536

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Monotone Valuations on the Space of Convex Functions

L. Cavallina
  • Corresponding author
  • Dipartimento di Matematica e Informatica “U.Dini", Viale Morgagni 67/A, 50134, Firenze, Italy
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ A. Colesanti
  • Corresponding author
  • Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-857, Japan
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-07-31 | DOI: https://doi.org/10.1515/agms-2015-0012


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.

Keywords: convex functions; valuations; convex bodies; sub-level sets; intrinsic volumes

MSC: 26B25; 52A41; 52B45


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About the article

Received: 2015-03-28

Accepted: 2015-06-16

Published Online: 2015-07-31

Citation Information: Analysis and Geometry in Metric Spaces, Volume 3, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2015-0012.

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© 2015 L. Cavallina and A. Colesanti. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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