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

Title:

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

Creator:

Kaliaj, Sokol B., Tato, Agron D., and Gumeni, Fatmir D.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:48df18e8-c1dc-40f9-90ac-a8aecbaee4d7
uuid:48df18e8-c1dc-40f9-90ac-a8aecbaee4d7

Subject:

Henstock-Kurzweil-Pettis integral, controlled convergence theorem, complete locally convex spaces, and $m$-dimensional compact interval

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

243-255

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:1

Harvested from:

CDK

Metadata only:

false