The McShane integral in weakly compactly generated spaces

被引：8

作者：

Aviles, A. ^{[2
]}

Plebanek, G. ^{[3
]}

Rodriguez, J. ^{[1
]}

机构：

[1] Univ Murcia, Dept Matemat Aplicada, Fac Informat, Espinardo 30100, Murcia, Spain

[2] Univ Murcia, Dept Math, Fac Matemat, Espinardo 30100, Murcia, Spain

[3] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 11期

关键词：

Pettis integral; McShane integral; Scalarly null function; Filling family; BANACH-SPACES; VALUED FUNCTIONS;

D O I：

10.1016/j.jfa.2010.08.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Di Piazza and Preiss asked whether every Pettis integrable function defined on [0, 1] and taking values in a weakly compactly generated Banach space is McShane integrable. In this paper we answer this question in the negative. Moreover, we give a counterexample where the target Banach space is reflexive. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2776 / 2792

页数：17

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