The research entitled “Integral Henstock-Kurzweil di Dalam Ruang C[Alfa,Beta]” was conducted by **Firdaus Ubaidillah** under the guidance of Prof. Dr. Soeparna Darmawijaya and Prof. Dr. Ch. Rini Indrati in 2017.

The following is the abstract of this research.

**ABSTRACT**

This dissertation is the result of research to construct of Henstock-Kurzweil type integral for space-valued functions that defined on a closed interval , where is the collection of all real-valued continuous functions defined on a closed interval . The concept of this integral follows Henstock-Kurzweil integral concept in the real space that has been known so far. We begin by introducing some fundamental concepts about the space , such as some properties of as a Riesz space, convergence of sequences and series, space-valued norms and metrics, and neighborhood of a point in . Furthermore, we construct calculus on for constructing Henstock-Kurzweil integral in the space such as limit, continuity, derivative of space-valued functions, and convergence of a sequence of functions. To construc the Henstock-Kurzweil integral of a space-valued function that defined on a closed interval , we begin by constructing a partition on . Furthermore, we define Henstock-Kurzweil integral of a space-valued function that defined on a closed interval . From this definition, we develop some properties of a Henstock-Kurzweil integrable function into theorems. From a Henstock-Kurzweil integrable function, we define a primitive of a Henstock-Kurzweil integrable function. To know some properties of a primitive of a Kurzweil-Henstock integrable function, we discuss the absolute Henstock-Kurzweil integral. In this dissertation, we give a brief discussion to Denjoy integral of space-valued functions. Further, we show that Denjoy integral is equivalent with Henstock-Kurzweil integral. To discuss this, we introduce the bounded variation function and the absolute continuous function. Finally, we discuss some convergence theorems of a sequence of Henstock-Kurzweil integrable functions. Our objective here is to prove that the monotone, uniform, controlled and dominated convergences of a sequence of Henstock-Kurzweil integral functions imply the convergence of the sequence formed by its corresponding integrals.

**Kata Kunci: **Henstock-Kurzweil integral, Henstock-Kurzweil primitive, bounded variation function, absolute continuous function, convergence theorem