Monotone Valuations on the Space of Convex Functions

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 continuit...

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Bibliographic Details
Main Authors:	Cavallina L., Colesanti A.
Format:	Article
Language:	English
Published:	De Gruyter 2015-07-01
Series:	Analysis and Geometry in Metric Spaces
Subjects:	convex functions valuations convex bodies sub-level sets intrinsic volumes 26b25; 52a41; 52b45
Online Access:	https://doi.org/10.1515/agms-2015-0012

id	doaj-d0e6cdcfb23947c8aff88a7535737026
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spelling	doaj-d0e6cdcfb23947c8aff88a75357370262021-09-06T19:39:45ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742015-07-013110.1515/agms-2015-0012agms-2015-0012Monotone Valuations on the Space of Convex FunctionsCavallina L.0Colesanti A.1Dipartimento di Matematica e Informatica “U.Dini", Viale Morgagni 67/A, 50134, Firenze, ItalyResearch Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-857, JapanWe 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.https://doi.org/10.1515/agms-2015-0012convex functions valuations convex bodies sub-level sets intrinsic volumes26b25; 52a41; 52b45
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Cavallina L. Colesanti A.
spellingShingle	Cavallina L. Colesanti A. Monotone Valuations on the Space of Convex Functions Analysis and Geometry in Metric Spaces convex functions valuations convex bodies sub-level sets intrinsic volumes 26b25; 52a41; 52b45
author_facet	Cavallina L. Colesanti A.
author_sort	Cavallina L.
title	Monotone Valuations on the Space of Convex Functions
title_short	Monotone Valuations on the Space of Convex Functions
title_full	Monotone Valuations on the Space of Convex Functions
title_fullStr	Monotone Valuations on the Space of Convex Functions
title_full_unstemmed	Monotone Valuations on the Space of Convex Functions
title_sort	monotone valuations on the space of convex functions
publisher	De Gruyter
series	Analysis and Geometry in Metric Spaces
issn	2299-3274
publishDate	2015-07-01
description	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.
topic	convex functions valuations convex bodies sub-level sets intrinsic volumes 26b25; 52a41; 52b45
url	https://doi.org/10.1515/agms-2015-0012
work_keys_str_mv	AT cavallinal monotonevaluationsonthespaceofconvexfunctions AT colesantia monotonevaluationsonthespaceofconvexfunctions
_version_	1717770135336386560

Monotone Valuations on the Space of Convex Functions

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