Henstock-kurzweil Integration: Its Relation To Topological Vector Spaces

Henstock-Kurzweil (HK) integration, which is based on integral sums, can be obtained by an inconspicuous change in the definition of Riemann integration. It is an extension of Lebesgue integration and there exists an HK-integrable function f such that its absolute value |f| is not HK-integrable. In this book HK integration is treated only on compact one-dimensional intervals.The set of convergent sequences of HK-integrable functions is singled out by an elementary convergence theorem. The concep