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

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 ℝ ^m and taking values in a Banach space. Then, we extend this theorem to complete locally convex topological vector spaces.