A homogeneous decomposition theorem for valuations on convex functions

被引：19
|
作者：
Colesanti, Andrea [1 ]
Ludwig, Monika [2 ]
Mussnig, Fabian [3 ]
机构：
[1] Univ Firenze, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy
[2] Tech Univ Wien, Inst Diskrete Math & Geometrie, Wiedner Hauptstr 8-10-1046, A-1040 Vienna, Austria
[3] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 279卷 / 05期
关键词：
Convex function; Valuation; Homogeneous decomposition; TRANSLATION INVARIANT VALUATIONS; SETS;
D O I：
10.1016/j.jfa.2020.108573
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree n are classified. By duality, corresponding results are obtained for valuations on finite-valued convex functions. (C) 2020 Elsevier Inc. All rights reserved.
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页数：25
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