A convergence theorem for $ap-$Henstock-Kurzweil integral and its relation to topology

Abstract

In this chapter we discuss about the  $ap-$Henstock-Kurzweil integrable functions on a topological vector spaces. Basic results of $ap-$Henstock-Kurzweil integrable functions are discussed here. We discuss the  equivalence of  the $ap-$Henstock-Kurzweil integral on a topological vector spaces and  the vector valued $ap-$Henstock-Kurzweil integral. Finally, several convergence theorems are studies.