Riemann-type definition of the improper integrals

Donatella Bongiorno

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 3, page 717-725
  • ISSN: 0011-4642

Abstract

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Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.

How to cite

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Bongiorno, Donatella. "Riemann-type definition of the improper integrals." Czechoslovak Mathematical Journal 54.3 (2004): 717-725. <http://eudml.org/doc/30894>.

@article{Bongiorno2004,
abstract = {Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.},
author = {Bongiorno, Donatella},
journal = {Czechoslovak Mathematical Journal},
keywords = {McShane’s partition; Kurzweil-Henstock’s partition; McShane partition; Kurzweil-Henstock partition},
language = {eng},
number = {3},
pages = {717-725},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Riemann-type definition of the improper integrals},
url = {http://eudml.org/doc/30894},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Bongiorno, Donatella
TI - Riemann-type definition of the improper integrals
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 3
SP - 717
EP - 725
AB - Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.
LA - eng
KW - McShane’s partition; Kurzweil-Henstock’s partition; McShane partition; Kurzweil-Henstock partition
UR - http://eudml.org/doc/30894
ER -

References

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  1. Un nuovo integrale per il problema delle primitive, Le Matematiche 51 (1996), 299–313. (1996) 
  2. 10.1112/S0024610700008905, J.  London Math. Soc. 62 (2000), 117–126. (2000) MR1771855DOI10.1112/S0024610700008905
  3. 10.4064/cm-50-2-289-293, Coll. Math. 50 (1986), 289–293. (1986) MR0857865DOI10.4064/cm-50-2-289-293
  4. The Integrals of Lebesgue, Denjoy, Perron, and Lebesgue. Graduate Studies in Math, vol. 4, AMS, 1994. (1994) MR1288751
  5. 10.2307/2319078, Amer. Math. Monthly 80 (1973), 349–359. (1973) Zbl0266.26008MR0318434DOI10.2307/2319078
  6. Nichtabsolut Konvergente Integrale, Teubner, Leipzig, 1980. (1980) Zbl0441.28001MR0597703
  7. The Riemann Approach to Integration, Cambridge Univ. Press, Cambridge, 1993. (1993) Zbl0804.26005MR1268404
  8. Theory of the Integral, Dover, New York, 1964. (1964) MR0167578

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