The McShane and the Pettis integral of Banach space-valued functions defined on Rm

被引：11

作者：

Ye, GJ ^{[1
]}

Schwabik, S

机构：

[1] NW Normal Univ, Coll Math & Informat Sci, Lanzhou 730070, Peoples R China

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

来源：

ILLINOIS JOURNAL OF MATHEMATICS | 2002年 / 46卷 / 04期

关键词：

D O I：

10.1215/ijm/1258138470

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we define and study the McShane integral of functions mapping a compact interval to I-o in R-m into a Banach space X. We compare this integral with the Pettis integral and prove, in particular, that the two integrals are equivalent if X is reflexive and the unit ball of the dual X* satisfies an additional condition (P). This gives additional information oil an implicitly stated open problem of R.A. Gordon and on the work of D.H. Fremlin and J. Mendoza.

引用

页码：1125 / 1144

页数：20

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