Bounded convergence theorem for abstract Kurzweil–Stieltjes integral

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00460232" target="_blank" >RIV/67985840:_____/16:00460232 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00605-015-0774-z" target="_blank" >http://dx.doi.org/10.1007/s00605-015-0774-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00605-015-0774-z" target="_blank" >10.1007/s00605-015-0774-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Bounded convergence theorem for abstract Kurzweil–Stieltjes integral

Popis výsledku v původním jazyce

In the theories of Lebesgue integration and of ordinary differential equations, the Lebesgue Dominated Convergence Theorem provides one of the most widely used tools. Available analogy in the Riemann or Riemann–Stieltjes integration is the Bounded Convergence Theorem, sometimes called also the Arzelà or Arzelà–Osgood or Osgood Theorem. In the setting of the Kurzweil–Stieltjes integral for real valued functions its proof can be obtained by a slight modification of the proof given for the ...-Young–Stieltjes integral by T.H. Hildebrandt in his monograph from 1963. However, it is clear that the Hildebrandt’s proof cannot be extended to the case of Banach space-valued functions. Moreover, it essentially utilizes the Arzelà Lemma which does not fit too much into elementary text-books. In this paper, we present the proof of the Bounded Convergence Theorem for the abstract Kurzweil–Stieltjes integral in a setting elementary as much as possible. In the theories of Lebesgue integration and of ordinary differential equations, the Lebesgue Dominated Convergence Theorem provides one of the most widely used tools. Available analogy in the Riemann or Riemann–Stieltjes integration is the Bounded Convergence Theorem, sometimes called also the Arzelà or Arzelà–Osgood or Osgood Theorem. In the setting of the Kurzweil–Stieltjes integral for real valued functions its proof can be obtained by a slight modification of the proof given for the ...-Young–Stieltjes integral by T.H. Hildebrandt in his monograph from 1963. However, it is clear that the Hildebrandt’s proof cannot be extended to the case of Banach space-valued functions. Moreover, it essentially utilizes the Arzelà Lemma which does not fit too much into elementary text-books. In this paper, we present the proof of the Bounded Convergence Theorem for the abstract Kurzweil–Stieltjes integral in a setting elementary as much as possible.

Název v anglickém jazyce

Bounded convergence theorem for abstract Kurzweil–Stieltjes integral

Popis výsledku anglicky

In the theories of Lebesgue integration and of ordinary differential equations, the Lebesgue Dominated Convergence Theorem provides one of the most widely used tools. Available analogy in the Riemann or Riemann–Stieltjes integration is the Bounded Convergence Theorem, sometimes called also the Arzelà or Arzelà–Osgood or Osgood Theorem. In the setting of the Kurzweil–Stieltjes integral for real valued functions its proof can be obtained by a slight modification of the proof given for the ...-Young–Stieltjes integral by T.H. Hildebrandt in his monograph from 1963. However, it is clear that the Hildebrandt’s proof cannot be extended to the case of Banach space-valued functions. Moreover, it essentially utilizes the Arzelà Lemma which does not fit too much into elementary text-books. In this paper, we present the proof of the Bounded Convergence Theorem for the abstract Kurzweil–Stieltjes integral in a setting elementary as much as possible. In the theories of Lebesgue integration and of ordinary differential equations, the Lebesgue Dominated Convergence Theorem provides one of the most widely used tools. Available analogy in the Riemann or Riemann–Stieltjes integration is the Bounded Convergence Theorem, sometimes called also the Arzelà or Arzelà–Osgood or Osgood Theorem. In the setting of the Kurzweil–Stieltjes integral for real valued functions its proof can be obtained by a slight modification of the proof given for the ...-Young–Stieltjes integral by T.H. Hildebrandt in his monograph from 1963. However, it is clear that the Hildebrandt’s proof cannot be extended to the case of Banach space-valued functions. Moreover, it essentially utilizes the Arzelà Lemma which does not fit too much into elementary text-books. In this paper, we present the proof of the Bounded Convergence Theorem for the abstract Kurzweil–Stieltjes integral in a setting elementary as much as possible.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA14-06958S" target="_blank" >GA14-06958S: Singularity a impulsy v okrajových úlohách pro nelineární obyčejné diferenciální rovnice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Monatshefte für Mathematik

ISSN

0026-9255

e-ISSN

—

Svazek periodika

180

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

AT - Rakouská republika

Počet stran výsledku

26

Strana od-do

409-434

Kód UT WoS článku

000378786900001

EID výsledku v databázi Scopus

2-s2.0-84931049667