On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals

Antonio Boccuto; Beloslav Riečan

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 3, page 591-607
  • ISSN: 0011-4642

Abstract

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In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with the usual one.

How to cite

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Boccuto, Antonio, and Riečan, Beloslav. "On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals." Czechoslovak Mathematical Journal 54.3 (2004): 591-607. <http://eudml.org/doc/30885>.

@article{Boccuto2004,
abstract = {In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with the usual one.},
author = {Boccuto, Antonio, Riečan, Beloslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {Riesz spaces; Henstock-Kurzweil integral; Riesz spaces; Henstock-Kurzweil integral},
language = {eng},
number = {3},
pages = {591-607},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals},
url = {http://eudml.org/doc/30885},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Boccuto, Antonio
AU - Riečan, Beloslav
TI - On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 3
SP - 591
EP - 607
AB - In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with the usual one.
LA - eng
KW - Riesz spaces; Henstock-Kurzweil integral; Riesz spaces; Henstock-Kurzweil integral
UR - http://eudml.org/doc/30885
ER -

References

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  8. Integral, Measure and Ordering, Kluwer Academic Publishers/Ister Science, 1997. (1997) MR1489521
  9. On the Kurzweil integral for functions with values in ordered spaces  II, Math. Slovaca 43 (1993), 471–475. (1993) MR1248980
  10. On integration with respect to operator valued measures in Riesz spaces, Tatra Mt. Math. Publ. 2 (1993), 149–165. (1993) MR1251049
  11. On the Kurzweil integral for functions with values in ordered spaces  III, Tatra Mt. Math. Publ. 8 (1996), 93–100. (1996) MR1475267
  12. 10.1023/A:1022483929348, Czechoslovak Math.  J. 48(123) (1998), 565–574. (1998) MR1637875DOI10.1023/A:1022483929348
  13. 10.5802/aif.393, Ann. Inst. Fourier Grenoble 21 (1971), 65–85. (1971) Zbl0215.48101MR0330411DOI10.5802/aif.393

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