On the strong McShane integral of functions with values in a Banach space

被引：11

作者：

Schwabik, S

Ye, GJ

机构：

[1] AV CR, Matemat Ustav, Prague 11567 1, Czech Republic

[2] NW Normal Univ, Lanzhou, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2001年 / 51卷 / 04期

关键词：

Bochner integral; strong McShane integral;

D O I：

10.1023/A:1013721114330

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions.

引用

页码：819 / 828

页数：10

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