On a generalization of Henstock-Kurzweil integrals

Jan Malý; Kristýna Kuncová

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 4, page 393-422
  • ISSN: 0862-7959

Abstract

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We study a scale of integrals on the real line motivated by the M C α integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.

How to cite

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Malý, Jan, and Kuncová, Kristýna. "On a generalization of Henstock-Kurzweil integrals." Mathematica Bohemica 144.4 (2019): 393-422. <http://eudml.org/doc/294370>.

@article{Malý2019,
abstract = {We study a scale of integrals on the real line motivated by the $MC_\{\alpha \}$ integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.},
author = {Malý, Jan, Kuncová, Kristýna},
journal = {Mathematica Bohemica},
keywords = {Henstock-Kurzweil integral},
language = {eng},
number = {4},
pages = {393-422},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a generalization of Henstock-Kurzweil integrals},
url = {http://eudml.org/doc/294370},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Malý, Jan
AU - Kuncová, Kristýna
TI - On a generalization of Henstock-Kurzweil integrals
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 4
SP - 393
EP - 422
AB - We study a scale of integrals on the real line motivated by the $MC_{\alpha }$ integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.
LA - eng
KW - Henstock-Kurzweil integral
UR - http://eudml.org/doc/294370
ER -

References

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