The Metric Integral of Set-Valued Functions

被引：4

作者：

Dyn, Nira ^{[1
]}

Farkhi, Elza ^{[1
,2
]}

Mokhov, Alona ^{[3
]}

机构：

[1] Tel Aviv Univ, Sch Math Sci, Tel Aviv, Israel

[2] Bulgarian Acad Sci, Inst Math & Informat, Sofia, Bulgaria

[3] Afeka Tel Aviv Acad Coll Engn, Unit Math, Tel Aviv, Israel

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2018年 / 26卷 / 04期

关键词：

Compact sets; Set-valued functions; Metric selections; Metric linear combinations; Aumann integral; Kuratowski upper limit; Metric integral; APPROXIMATIONS;

D O I：

10.1007/s11228-017-0403-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper introduces a new integral of univariate set-valued functions of bounded variation with compact images in R-d. The new integral, termed the metric integral, is defined using metric linear combinations of sets and is shown to consist of integrals of all the metric selections of the integrated multifunction. The metric integral is a subset of the Aumann integral, but in contrast to the latter, it is not necessarily convex. For a special class of segment functions equality of the two integrals is shown. Properties of the metric selections and related properties of the metric integral are studied. Several indicative examples are presented.

引用

页码：867 / 885

页数：19

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