Controlled Convergence Theorem for Strong Variational Banach-Valued Multiple Integrals
Lorna I. Paredes, Lee Peng Yee, Chew Tuan Seng · Real Analysis Exchange · 2003
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].