Variational Henstock integrability of Banach space valued functions

Title:

Variational Henstock integrability of Banach space valued functions

Creator:

Di Piazza, Luisa, Marraffa, Valeria, and Musiał, Kazimierz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1acf14ee-0d2f-4b8f-91f1-ae9511f0a18b
uuid:1acf14ee-0d2f-4b8f-91f1-ae9511f0a18b
doi:10.21136/MB.2016.19

Subject:

Kurzweil-Henstock integral, variational Henstock integral, and Pettis integral

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study the integrability of Banach space valued strongly measurable functions defined on [0, 1]. In the case of functions f given by ∑ ∞ n=1 xnχEn , where xn are points of a Banach space and the sets En are Lebesgue measurable and pairwise disjoint subsets of [0, 1], there are well known characterizations for Bochner and Pettis integrability of f. The function f is Bochner integrable if and only if the series ∑∞ n=1 xn|En| is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability of f. In this paper we give some conditions for variational Henstock integrability of a certain class of such functions.

Language:

English

Rights:

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

Coverage:

287-296

Source:

Mathematica bohemica | 2016 Volume:141 | Number:2

Harvested from:

CDK

Metadata only:

false