Monotone Valuations on the Space of Convex Functions

L. Cavallina; A. Colesanti

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 167-211, electronic only
  • ISSN: 2299-3274

Abstract

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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.

How to cite

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L. Cavallina, and A. Colesanti. "Monotone Valuations on the Space of Convex Functions." Analysis and Geometry in Metric Spaces 3.1 (2015): 167-211, electronic only. <http://eudml.org/doc/271207>.

@article{L2015,
abstract = {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.},
author = {L. Cavallina, A. Colesanti},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {convex functions; valuations; convex bodies; sub-level sets; intrinsic volumes},
language = {eng},
number = {1},
pages = {167-211, electronic only},
title = {Monotone Valuations on the Space of Convex Functions},
url = {http://eudml.org/doc/271207},
volume = {3},
year = {2015},
}

TY - JOUR
AU - L. Cavallina
AU - A. Colesanti
TI - Monotone Valuations on the Space of Convex Functions
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 167
EP - 211, electronic only
AB - 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.
LA - eng
KW - convex functions; valuations; convex bodies; sub-level sets; intrinsic volumes
UR - http://eudml.org/doc/271207
ER -

References

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