JournalszaaVol. 13, No. 4pp. 567–576

Sequential Convergence in the Space of Absolutely Riemann Integrable Functions

  • M.A. Jiménez

    Universidad de La Habana, Cuba
  • E. López

    Instituto Pedagógico La Habana, Cuba
  • J.-J. Rückmann

    Humboldt-Universität zu Berlin, Germany
Sequential Convergence in the Space of Absolutely Riemann Integrable Functions cover
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Abstract

The concept of RR-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.

Cite this article

M.A. Jiménez, E. López, J.-J. Rückmann, Sequential Convergence in the Space of Absolutely Riemann Integrable Functions. Z. Anal. Anwend. 13 (1994), no. 4, pp. 567–576

DOI 10.4171/ZAA/493