On Kurzweil-Henstock equiintegrable sequences

Štefan Schwabik; Ivo Vrkoč

Mathematica Bohemica (1996)

  • Volume: 121, Issue: 2, page 189-207
  • ISSN: 0862-7959

Abstract

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For the Kurzweil-Henstock integral the equiintegrability of a pointwise convergent sequence of integrable functions implies the integrability of the limit function and the relation m abfm(s)s = abm fm(s)s. Conditions for the equiintegrability of a sequence of functions pointwise convergent to an integrable function are presented. These conditions are given in terms of convergence of some sequences of integrals.

How to cite

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Schwabik, Štefan, and Vrkoč, Ivo. "On Kurzweil-Henstock equiintegrable sequences." Mathematica Bohemica 121.2 (1996): 189-207. <http://eudml.org/doc/247970>.

@article{Schwabik1996,
abstract = {For the Kurzweil-Henstock integral the equiintegrability of a pointwise convergent sequence of integrable functions implies the integrability of the limit function and the relation m abfm(s)s = abm fm(s)s. Conditions for the equiintegrability of a sequence of functions pointwise convergent to an integrable function are presented. These conditions are given in terms of convergence of some sequences of integrals.},
author = {Schwabik, Štefan, Vrkoč, Ivo},
journal = {Mathematica Bohemica},
keywords = {equiintegrable sequence; Kurzweil-Henstock integral; equiintegrable sequence; Kurzweil-Henstock integral},
language = {eng},
number = {2},
pages = {189-207},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Kurzweil-Henstock equiintegrable sequences},
url = {http://eudml.org/doc/247970},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Schwabik, Štefan
AU - Vrkoč, Ivo
TI - On Kurzweil-Henstock equiintegrable sequences
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 2
SP - 189
EP - 207
AB - For the Kurzweil-Henstock integral the equiintegrability of a pointwise convergent sequence of integrable functions implies the integrability of the limit function and the relation m abfm(s)s = abm fm(s)s. Conditions for the equiintegrability of a sequence of functions pointwise convergent to an integrable function are presented. These conditions are given in terms of convergence of some sequences of integrals.
LA - eng
KW - equiintegrable sequence; Kurzweil-Henstock integral; equiintegrable sequence; Kurzweil-Henstock integral
UR - http://eudml.org/doc/247970
ER -

References

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  1. Gordon R. A., 10.2307/44152048, Real Analysis Exchange 15 (1989-90), 724-728. (1989) MR1059433DOI10.2307/44152048
  2. Gordon R. A., 10.1112/jlms/s2-44.2.301, J. London Math. Soc. 44 (1991), 301-309. (1991) MR1136442DOI10.1112/jlms/s2-44.2.301
  3. Gordon R. A., 10.1090/gsm/004/09, Graduate Studies in Math., Vol. 4, American Mathematical Society, 1994. (1994) Zbl0807.26004MR1288751DOI10.1090/gsm/004/09
  4. Henstock R., Lectures on the Theory of Integration, Series in Real Analysis, Vol. 1, World Scientific, Singapore, 1988. (1988) Zbl0668.28001MR0963249
  5. Kurzweil J., Nichtabsolut konvergente Integrale, Teubner-Texte zur Mathematik, Band 26, Teubner, Leipzig, 1980. (1980) Zbl0441.28001MR0597703
  6. Kurzweil J., Jarník J., Equiintegrability and controlled convergence of Perron-type integrable functions, Real Anal. Exchange П (1991-92), 110-139. (1991) 
  7. Lee Peng Yee, Lanzhou Lectures on Henstock Integration, Series in Real Analysis, Vol. 2, World Scientific, Singapore, 1989. (1989) Zbl0699.26004MR1050957
  8. McLeod R. M., The Generalized Riemann Integral, Caгus Mathematical Monographs, No. 20, Mathematical Association of America, 1980. (1980) Zbl0486.26005MR0588510
  9. Schwabik Š., Generalized Ordinary Differential Equations, Series in Real Analysis, Vol. 5, World Scientific, Singapore, 1992. (1992) Zbl0781.34003MR1200241
  10. Schwabik Š., Convergence theorems for the Perron integral and Sklyarenko's condition, Comment. Math. Univ. Carolin. 33,2 (1992), 237-244. (1992) Zbl0774.26004MR1189654

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