On the Henstock-Kurzweil Integral of C [a; b] Space-valued Functions

Abstract

Let C[a; b] be the set of all real-valued continuous functions de ned on a closed interval [a; b] R. In this paper, we construct the HenstockKurzweil integral on a closed interval [f; g] C[a; b] and investigate some of its properties of the Henstock-Kurzweil integral. Futhermore, we prove a monotone convergence theorem of the Henstock-Kurzweil integral on C[a; b].