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

被引：0
作者：
Sokol B. Kaliaj
Agron D. Tato
Fatmir D. Gumeni
机构：
[1] University of Elbasan,
[2] Planetar University of Tirana,undefined
来源：
Czechoslovak Mathematical Journal | 2012年 / 62卷
关键词：
Henstock-Kurzweil-Pettis integral; controlled convergence theorem; complete locally convex spaces; -dimensional compact interval; 28B05; 46G10;
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摘要：
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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页码：243 / 255
页数：12
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