Sequential Convergence in the Space of Absolutely Riemann Integrable Functions

Abstract

The concept of $R$-convergence in the space of usual Riemann integrable functions was introduced by Dickmeis, Mevissen, Nessel and van Wickeren in 1986. They proved that this space, provided with R-convergence, is sequentially complete and that every function in the space can be approximated by a sequence of continuous functions. They gave several applications. This paper extends that concept to the space of absolutely Riemann integrable functions and it is shown that the results mentioned above still hold there.