A simplified multidimensional integral

Ágnes M. Backhausz; Vilmos Komornik; Tivadar Szilágyi

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 3, page 721-739
  • ISSN: 0011-4642

Abstract

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We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.

How to cite

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Backhausz, Ágnes M., Komornik, Vilmos, and Szilágyi, Tivadar. "A simplified multidimensional integral." Czechoslovak Mathematical Journal 59.3 (2009): 721-739. <http://eudml.org/doc/37954>.

@article{Backhausz2009,
abstract = {We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.},
author = {Backhausz, Ágnes M., Komornik, Vilmos, Szilágyi, Tivadar},
journal = {Czechoslovak Mathematical Journal},
keywords = {integral of several variables; characterization of primitives; integral of several variables; characterization of primitives},
language = {eng},
number = {3},
pages = {721-739},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A simplified multidimensional integral},
url = {http://eudml.org/doc/37954},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Backhausz, Ágnes M.
AU - Komornik, Vilmos
AU - Szilágyi, Tivadar
TI - A simplified multidimensional integral
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 721
EP - 739
AB - We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
LA - eng
KW - integral of several variables; characterization of primitives; integral of several variables; characterization of primitives
UR - http://eudml.org/doc/37954
ER -

References

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  1. Bartle, R. G., A Modern Theory of Integration, Amer. Math. Society, Providence, Rhode Island (2001). (2001) Zbl0968.26001MR1817647
  2. Botsko, M. W., 10.2307/2324087, Amer. Math. Monthly 96 (1989), 328-333. (1989) Zbl0721.26003MR0992079DOI10.2307/2324087
  3. Dieudonné, J., Foundations of Modern Analysis, Academic Press, New York and London (1969). (1969) MR0349288
  4. Pfeffer, Washek F., The Riemann Approach to Integration: Local Geometric Theory Cambridge University Press, Cambridge, (1993). (1993) MR1268404

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