On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals

Title:

On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals

Creator:

Racca, Abraham and Cabral, Emmanuel

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:9131dc32-af01-4149-81b3-063dd319596b
uuid:9131dc32-af01-4149-81b3-063dd319596b
doi:10.21136/MB.2016.13

Subject:

Kurzweil-Henstock integral, g-integral, double Lusin condition, and uniform double Lusin condition

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Equiintegrability in a compact interval E may be defined as a uniform integrability property that involves both the integrand fn and the corresponding primitive Fn. The pointwise convergence of the integrands fn to some f and the equiintegrability of the functions fn together imply that f is also integrable with primitive F and that the primitives Fn converge uniformly to F. In this paper, another uniform integrability property called uniform double Lusin condition introduced in the papers E. Cabral and P. Y. Lee (2001/2002) is revisited. Under the assumption of pointwise convergence of the integrands fn, the three uniform integrability properties, namely equiintegrability and the two versions of the uniform double Lusin condition, are all equivalent. The first version of the double Lusin condition and its corresponding uniform double Lusin convergence theorem are also extended into the division space.

Language:

English

Rights:

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

Coverage:

153-168

Source:

Mathematica bohemica | 2016 Volume:141 | Number:2

Harvested from:

CDK

Metadata only:

false