On the limits of generalization of the Kolmogorov integral

被引：10

作者：

Solodov, AP ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow 117234, Russia

来源：

MATHEMATICAL NOTES | 2005年 / 77卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

Kolmogorov integral; Banach space; Bochner integral; McShane integral; henstock integral; lebesgue integral; lebesgue measure;

D O I：

10.1007/s11006-005-0023-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The generalization of the Kolmogorov integral to functions with values in a Banach space is considered. It is proved that the resulting integral turns out to be essentially more general than the Bochner integral and is exactly equivalent to an integral of McShane type, whose definition requires that the scaling function be measurable.

引用

页码：232 / 245

页数：14

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