The Vitali convergence theorem for the vector-valued McShane integral

Title:

The Vitali convergence theorem for the vector-valued McShane integral

Creator:

Reynolds, Richard and Swartz, Charles

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a37ce69a-f316-4178-8334-c460e07778ca
uuid:a37ce69a-f316-4178-8334-c460e07778ca
doi:10.21136/MB.2004.133906

Subject:

vector-valued McShane integral, Vitali theorem, and norm convergence

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The classical Vitali convergence theorem gives necessary and sufficient conditions for norm convergence in the space of Lebesgue integrable functions. Although there are versions of the Vitali convergence theorem for the vector valued McShane and Pettis integrals given by Fremlin and Mendoza, these results do not involve norm convergence in the respective spaces. There is a version of the Vitali convergence theorem for scalar valued functions defined on compact intervals in Rn given by Kurzweil and Schwabik, but again this version does not consider norm convergence in the space of integrable functions. In this paper we give a version of the Vitali convergence theorem for norm convergence in the space of vector-valued McShane integrable functions.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

159-176

Source:

Mathematica bohemica | 2004 Volume:129 | Number:2

Harvested from:

CDK

Metadata only:

false