A step to Kurzweil-Henstock—an outline

B. D. Craven

Mathematica Bohemica (2004)

  • Volume: 129, Issue: 3, page 297-304
  • ISSN: 0862-7959

Abstract

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A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish.

How to cite

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Craven, B. D.. "A step to Kurzweil-Henstock—an outline." Mathematica Bohemica 129.3 (2004): 297-304. <http://eudml.org/doc/249402>.

@article{Craven2004,
abstract = {A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish.},
author = {Craven, B. D.},
journal = {Mathematica Bohemica},
keywords = {integral; Kurzweil-Henstock integral; step-function; filterbase; Kurzweil-Henstock integral; step-function; filterbase},
language = {eng},
number = {3},
pages = {297-304},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A step to Kurzweil-Henstock—an outline},
url = {http://eudml.org/doc/249402},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Craven, B. D.
TI - A step to Kurzweil-Henstock—an outline
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 3
SP - 297
EP - 304
AB - A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish.
LA - eng
KW - integral; Kurzweil-Henstock integral; step-function; filterbase; Kurzweil-Henstock integral; step-function; filterbase
UR - http://eudml.org/doc/249402
ER -

References

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  1. Lebesgue Measure and Integral, Pitman, Boston, 1982. (1982) Zbl0491.28001MR0733102
  2. Topology, Allyn & Bacon, Boston, 1966. (1966) Zbl0144.21501MR0193606
  3. Linear Analysis, Butterworths, 1967. (1967) Zbl0172.39001MR0419707
  4. The General Theory of Integration, Clarendon Press, Oxford, U.K., 1991. (1991) Zbl0745.26006MR1134656
  5. Nichtabsolut konvergente Intgegrale, Teubner, Leipzig, 1980. (1980) MR0597703
  6. The Kurzweil-Henstock Integral and its Differentials, Marcel Dekker, New York, 2001. (2001) Zbl0984.26002MR1837270
  7. Lanzhou Lectures on Integration, World Scientific, Singapore, 1989. (1989) MR1050957
  8. The Integral: an easy approach after Kurzweil and Henstock, Cambridge University Press, 2000. (2000) MR1756319
  9. Handbook of Analysis and its Foundations, Academic Press, San Diego, 1997 (Chapter 24: Generalized Riemann integrals). (1997 (Chapter 24: Generalized Riemann integrals)) MR1417259
  10. Integration on : Kurzweil Theory, Charles University, Praha, 1999. (Czech) (1999) 

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