Role of the Harnack extension principle in the Kurzweil-Stieltjes integral

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00599944" target="_blank" >RIV/67985840:_____/24:00599944 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.21136/MB.2023.0162-22" target="_blank" >https://doi.org/10.21136/MB.2023.0162-22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/MB.2023.0162-22" target="_blank" >10.21136/MB.2023.0162-22</a>

Result language

angličtina

Original language name

Role of the Harnack extension principle in the Kurzweil-Stieltjes integral

Original language description

In the theories of integration and of ordinary differential and integral equations, convergence theorems provide one of the most widely used tools. Since the values of the Kurzweil-Stieltjes integrals over various kinds of bounded intervals having the same infimum and supremum need not coincide, the Harnack extension principle in the Kurzweil-Henstock integral, which is a key step to supply convergence theorems, cannot be easily extended to the Kurzweil-type Stieltjes integrals with discontinuous integrators. Moreover, in general, the existence of integral over an elementary set E does not always imply the existence of integral over every subset T of E. The goal of this paper is to construct the Harnack extension principle for the Kurzweil-Stieltjes integral with values in Banach spaces and then to demonstrate its role in guaranteeing the integrability over arbitrary subsets of elementary sets. New concepts of equiintegrability and equiregulatedness involving elementary sets are pivotal to the notion of the Harnack extension principle for the Kurzweil-Stieltjes integration.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematica Bohemica

ISSN

0862-7959

e-ISSN

2464-7136

Volume of the periodical

149

Issue of the periodical within the volume

3

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

27

Pages from-to

337-363

UT code for WoS article

001034335700001

EID of the result in the Scopus database

2-s2.0-85205862547