Controlled convergence theorem for strong variational Banach-valued multiple integrals. (English) Zbl 1059.28013

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

Real Anal. Exch. 28(2002-2003), No. 2, 579-591 (2003).

The authors prove a controlled convergence theorem for \(n\)-dimensional strong variational Banach-space valued integrals. The proof is different from that in the 1-dimensional case published in [Sci. Math. Jpn. 56, No. 2, 347–357 (2002; Zbl 1026.28013)] by L. I. Paredes and T. S. Chew.

Reviewer: Kazimierz Musiał(Wrocław)

MSC:

28B05	Vector-valued set functions, measures and integrals
26A39	Denjoy and Perron integrals, other special integrals
46G10	Vector-valued measures and integration

Keywords:

Henstock integral; HL -integral; ML integral; variational Banach space valued multiple integrals; controlled convergence

Citations:

Zbl 1026.28013