Convergence theorems for the Perron integral and Sklyarenko's condition

Štefan Schwabik

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 2, page 237-244
  • ISSN: 0010-2628

Abstract

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It is shown that a uniform version of Sklyarenko's integrability condition for Perron integrals together with pointwise convergence of a sequence of integrable functions are sufficient for a convergence theorem for Perron integrals.

How to cite

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Schwabik, Štefan. "Convergence theorems for the Perron integral and Sklyarenko's condition." Commentationes Mathematicae Universitatis Carolinae 33.2 (1992): 237-244. <http://eudml.org/doc/247399>.

@article{Schwabik1992,
abstract = {It is shown that a uniform version of Sklyarenko's integrability condition for Perron integrals together with pointwise convergence of a sequence of integrable functions are sufficient for a convergence theorem for Perron integrals.},
author = {Schwabik, Štefan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Kurzweil-Henstock integral; Perron integral; Sklyarenko integrability condition; Perron integral; equi-integrability; convergence theorems; Kurzweil-Henstock integral},
language = {eng},
number = {2},
pages = {237-244},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Convergence theorems for the Perron integral and Sklyarenko's condition},
url = {http://eudml.org/doc/247399},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Schwabik, Štefan
TI - Convergence theorems for the Perron integral and Sklyarenko's condition
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 2
SP - 237
EP - 244
AB - It is shown that a uniform version of Sklyarenko's integrability condition for Perron integrals together with pointwise convergence of a sequence of integrable functions are sufficient for a convergence theorem for Perron integrals.
LA - eng
KW - Kurzweil-Henstock integral; Perron integral; Sklyarenko integrability condition; Perron integral; equi-integrability; convergence theorems; Kurzweil-Henstock integral
UR - http://eudml.org/doc/247399
ER -

References

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  1. Henstock R., Lectures on the Theory of Integration, World Scientific Singapore (1988). (1988) Zbl0668.28001MR0963249
  2. Henstock R., The General Theory of Integration, Clarendon Press Oxford (1991). (1991) Zbl0745.26006MR1134656
  3. Kurzweil J., Nichtabsolut konvergente Integrale, BSB B.G. Teubner Verlagsgesellschaft Leipzig (1980). (1980) Zbl0441.28001MR0597703
  4. Lee Peng-Yee, Lanzhou Lectures on Henstock Integration, World Scientific Singapore (1989). (1989) Zbl0699.26004MR1050957
  5. Mawhin J., Introduction à l'Analyse, CABAY, Libraire-éditeur Louvain-La-Neuve (1984). (1984) 
  6. McLeod R.M., The Generalized Riemann Integral, Math. Assoc. of America (1980). (1980) Zbl0486.26005MR0588510
  7. Preiss D., Schwabik Š., The definite integral, Mimeographed notes in Czech Math.-Phys. Fac. of the Charles Univ. and Math. Inst. of the Czech. Acad. Sci Prague (1979), 138 pages. (1979) 
  8. Saks S., Theory of the integral, Warszawa (1937). (1937) Zbl0017.30004
  9. Sklyarenko V.A., On integration by parts for Burkill's SCP-integral, Mat. Sbornik 630-646 (1980), 112. (1980) MR0587041
  10. Thomson B.S., Derivation bases on the real line (II), Real Analysis Exchange 8 278-442 (1982-83). (1982-83) Zbl0525.26003MR0700194

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