On McShane-type integrals with respect to some derivation bases

Valentin A. Skvortsov; Piotr Sworowski

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 4, page 365-378
  • ISSN: 0862-7959

Abstract

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Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in ℝ n is given.

How to cite

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Skvortsov, Valentin A., and Sworowski, Piotr. "On McShane-type integrals with respect to some derivation bases." Mathematica Bohemica 131.4 (2006): 365-378. <http://eudml.org/doc/249897>.

@article{Skvortsov2006,
abstract = {Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in $\mathbb \{R\}^n$ is given.},
author = {Skvortsov, Valentin A., Sworowski, Piotr},
journal = {Mathematica Bohemica},
keywords = {McShane integral; Kurzweil-Henstock integral; Perron integral; basis; McShane integral; Kurzweil-Henstock integral; Perron integral},
language = {eng},
number = {4},
pages = {365-378},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On McShane-type integrals with respect to some derivation bases},
url = {http://eudml.org/doc/249897},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Skvortsov, Valentin A.
AU - Sworowski, Piotr
TI - On McShane-type integrals with respect to some derivation bases
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 4
SP - 365
EP - 378
AB - Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in $\mathbb {R}^n$ is given.
LA - eng
KW - McShane integral; Kurzweil-Henstock integral; Perron integral; basis; McShane integral; Kurzweil-Henstock integral; Perron integral
UR - http://eudml.org/doc/249897
ER -

References

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  7. 10.1007/s10587-004-6407-7, Czechoslovak Math. J. 54 (2004), 545–557. (2004) MR2086715DOI10.1007/s10587-004-6407-7
  8. The Riemann Approach to Integration, Cambridge University Press, Cambridge, 1993. (1993) Zbl0804.26005MR1268404
  9. Continuity of δ -variation and construction of continuous major and minor functions for the Perron integral, Real Anal. Exchange 21 (1995/96), 270–277. (1995/96) MR1377536
  10. Real Functions, Lecture Notes in Mathematics, vol. 1170, Springer, 1985. (1985) Zbl0581.26001MR0818744
  11. Symmetric Properties of Real Functions, Monographs and Textbooks in Pure and Applied Mathematics, vol. 183, Marcel Dekker, New York, 1994. (1994) Zbl0809.26001MR1289417
  12. An integral involving Thomson’s local systems, Real Anal. Exchange 19 (1993/94), 248–253. (1993/94) MR1268851

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