The Kurzweil integral with exclusion of negligible sets

Pavel Krejčí

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 3, page 277-292
  • ISSN: 0862-7959

Abstract

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We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of δ -fine partitions by excluding small sets.

How to cite

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Krejčí, Pavel. "The Kurzweil integral with exclusion of negligible sets." Mathematica Bohemica 128.3 (2003): 277-292. <http://eudml.org/doc/249241>.

@article{Krejčí2003,
abstract = {We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of $\delta $-fine partitions by excluding small sets.},
author = {Krejčí, Pavel},
journal = {Mathematica Bohemica},
keywords = {Kurzweil integral; Young integral; Kurzweil integral; Young integral},
language = {eng},
number = {3},
pages = {277-292},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Kurzweil integral with exclusion of negligible sets},
url = {http://eudml.org/doc/249241},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Krejčí, Pavel
TI - The Kurzweil integral with exclusion of negligible sets
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 3
SP - 277
EP - 292
AB - We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of $\delta $-fine partitions by excluding small sets.
LA - eng
KW - Kurzweil integral; Young integral; Kurzweil integral; Young integral
UR - http://eudml.org/doc/249241
ER -

References

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  7. On the relation between Young’s and Kurzweil’s concept of Stieltjes integral, Čas. Pěst. Mat. 98 (1973), 237–251. (1973) Zbl0266.26006MR0322113
  8. On a modified sum integral of Stieltjes type, Čas. Pěst. Mat. 98 (1973), 274–277. (1973) Zbl0266.26007MR0322114
  9. Abstract Perron-Stieltjes integral, Math. Bohem. 121 (1996), 425–447. (1996) Zbl0879.28021MR1428144
  10. Regulated functions and the Perron-Stieltjes integral, Čas. Pěst. Mat. 114 (1989), 187–209. (1989) MR1063765

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