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

Kaliaj, Sokol B., Tato, Agron D., and Gumeni, Fatmir D.. "Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on $m$-dimensional compact intervals." Czechoslovak Mathematical Journal 62.1 (2012): 243-255. <http://eudml.org/doc/246260>.

@article{Kaliaj2012,
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 $\mathbb \{R\}^\{m\}$ and taking values in a Banach space. Then, we extend this theorem to complete locally convex topological vector spaces.},
author = {Kaliaj, Sokol B., Tato, Agron D., Gumeni, Fatmir D.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Henstock-Kurzweil-Pettis integral; controlled convergence theorem; complete locally convex spaces; $m$-dimensional compact interval; Henstock-Kurzweil-Pettis integral; controlled convergence theorem; complete locally convex spaces; -dimensional compact interval},
language = {eng},
number = {1},
pages = {243-255},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on $m$-dimensional compact intervals},
url = {http://eudml.org/doc/246260},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Kaliaj, Sokol B.
AU - Tato, Agron D.
AU - Gumeni, Fatmir D.
TI - Controlled convergence theorems for Henstock-Kurzweil-Pettis integral on $m$-dimensional compact intervals
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 243
EP - 255
AB - 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 $\mathbb {R}^{m}$ and taking values in a Banach space. Then, we extend this theorem to complete locally convex topological vector spaces.
LA - eng
KW - Henstock-Kurzweil-Pettis integral; controlled convergence theorem; complete locally convex spaces; $m$-dimensional compact interval; Henstock-Kurzweil-Pettis integral; controlled convergence theorem; complete locally convex spaces; -dimensional compact interval
UR - http://eudml.org/doc/246260
ER -