A Daniell integral approach to nonstandard Kurzweil-Henstock integral

Ricardo Bianconi; João C. Prandini; Cláudio Possani

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 4, page 817-823
  • ISSN: 0011-4642

Abstract

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A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results.

How to cite

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Bianconi, Ricardo, Prandini, João C., and Possani, Cláudio. "A Daniell integral approach to nonstandard Kurzweil-Henstock integral." Czechoslovak Mathematical Journal 49.4 (1999): 817-823. <http://eudml.org/doc/30525>.

@article{Bianconi1999,
abstract = {A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results.},
author = {Bianconi, Ricardo, Prandini, João C., Possani, Cláudio},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonstandard analysis; Kurzweil-Henstock integral; Daniell integral},
language = {eng},
number = {4},
pages = {817-823},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Daniell integral approach to nonstandard Kurzweil-Henstock integral},
url = {http://eudml.org/doc/30525},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Bianconi, Ricardo
AU - Prandini, João C.
AU - Possani, Cláudio
TI - A Daniell integral approach to nonstandard Kurzweil-Henstock integral
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 4
SP - 817
EP - 823
AB - A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results.
LA - eng
KW - nonstandard analysis; Kurzweil-Henstock integral; Daniell integral
UR - http://eudml.org/doc/30525
ER -

References

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  1. Nonstandard methods in stochastic analysis and mathematical physics, Academic Press, Orlando, 1986. (1986) MR0859372
  2. Superinfinitesimals and the calculus of the generalized Riemann integral, Models and sets (Aachen, 1983), Lect. Notes in Math., 1103, Springer, Berlin-New York, pp. 9–52. Zbl0583.26005MR0775686
  3. A note on frameworks of nonstandard analysis, in preparation, . 
  4. Nonstandard Henstock-Kurzweil integralProc. 42nd. SBA, (1995, 669–681). (1995, 669–681) 
  5. Review of, Mathematical Reviews, 86g:26008. 
  6. Lectures on the theory of integration, Series in Real Analysis Volume 1, World Scientific, Singapore, 1988. (1988) Zbl0668.28001MR0963249
  7. An introduction to nonstandard real analysis, Academic Press, Orlando, 1985. (1985) MR0806135
  8. Elementary calculus, Prindle, Weber and Schmidt, Boston, 1976. (1976) Zbl0325.26001
  9. Lanzhou lectures on Henstock integration, Series in Real Analysis Volume 2, World Scientific, Singapore, 1989. (1989) Zbl0699.26004MR1050957
  10. Generalized ordinary differential equations, Series in Real Analysis Volume 5, World Scientific, Singapore, 1992. (1992) Zbl0781.34003MR1200241

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