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Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on m-dimensional compact intervals

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Abstract

In this paper we use a generalized version of absolute continuity defined by J. Kurzweil, J. Jarník, Equiintegrability and controlled convergence of Perron-type integrable functions, Real Anal. Exch. 17 (1992), 110–139. By applying uniformly this generalized version of absolute continuity to the primitives of the Henstock-Kurzweil-Pettis integrable functions, we obtain controlled convergence theorems for the Henstock-Kurzweil-Pettis integral. First, we present a controlled convergence theorem for Henstock-Kurzweil-Pettis integral of functions defined on m-dimensional compact intervals of ℝm and taking values in a Banach space. Then, we extend this theorem to complete locally convex topological vector spaces.

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Authors and Affiliations

  1. University of Elbasan, Elbasan, Albania

    Sokol B. Kaliaj & Agron D. Tato

  2. Planetar University of Tirana, Tirana, Albania

    Fatmir D. Gumeni

Authors
  1. Sokol B. Kaliaj
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  2. Agron D. Tato
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  3. Fatmir D. Gumeni
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Correspondence to Sokol B. Kaliaj.

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Kaliaj, S.B., Tato, A.D. & Gumeni, F.D. Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on m-dimensional compact intervals. Czech Math J 62, 243–255 (2012). https://doi.org/10.1007/s10587-012-0009-6

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  • DOI: https://doi.org/10.1007/s10587-012-0009-6

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