A generalization of the set averaging theorem

被引：2

作者：

Ivanov, G. M. ^{[1
]}

Polovinkin, E. S. ^{[1
]}

机构：

[1] Moscow Inst Phys & Technol, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2012年 / 92卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

set averaging theorem; n-dimensional Euclidean space; Banach space; Riemann integral; non-convex-valued multivalued mapping; convex compact set; Hausdorff metric;

D O I：

10.1134/S000143461209009X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the possibility of generalizing the averaging theorem from the case of sets from n-dimensional Euclidean space to the case of sets from Banach spaces. The result is a cornerstone for constructing the theory of the Riemann integral for non-convex-valued multivalued mappings and for proving the convexity of this multivalued integral. We obtain a generalization of the averaging theorem to the case of sets from uniformly smooth Banach spaces as well as some corollaries.

引用

页码：369 / 374

页数：6

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