Real Analysis Exchange

Controlled convergence theorem for strong variational Banach-valued multiple integrals.

Lorna I. Paredes, Chew Tuan Seng, and Lee Peng Yee

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Abstract

In this paper, a controlled convergence theorem is proved for \(n\)-dimensional strong variational Banach-valued integrals, also referred herein as Banach-valued Multiple Integrals. The methods used in the proof for one dimensional case given in [15], in which linearization was used, cannot be applied for the higher dimensional case. Instead, we follow the ideas in [17, Chapter 5, Section 21; 4; 18].

Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 579-592.

Dates
First available in Project Euclid: 20 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184963819

Mathematical Reviews number (MathSciNet)
MR2010339

Zentralblatt MATH identifier
1059.28013

Subjects
Primary: 26A39: Denjoy and Perron integrals, other special integrals

Keywords
Henstock's integral Banach-valued integral controlled convergence theorem

Citation

Paredes, Lorna I.; Yee, Lee Peng; Seng, Chew Tuan. Controlled convergence theorem for strong variational Banach-valued multiple integrals. Real Anal. Exchange 28 (2002), no. 2, 579--592. https://projecteuclid.org/euclid.rae/1184963819


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