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 , 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].
"Controlled convergence theorem for strong variational Banach-valued multiple integrals.." Real Anal. Exchange 28 (2) 579 - 592, 2002/2003.