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.

引用

页数：25

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