Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space

Lee Tuo-Yeong

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 3, page 625-637
  • ISSN: 0011-4642

Abstract

top
Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.

How to cite

top

Tuo-Yeong, Lee. "Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space." Czechoslovak Mathematical Journal 55.3 (2005): 625-637. <http://eudml.org/doc/30973>.

@article{Tuo2005,
abstract = {Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.},
author = {Tuo-Yeong, Lee},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized absolute continuity; Henstock-Kurzweil integral; generalized absolute continuity; Henstock-Kurzweil integral},
language = {eng},
number = {3},
pages = {625-637},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space},
url = {http://eudml.org/doc/30973},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Tuo-Yeong, Lee
TI - Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 3
SP - 625
EP - 637
AB - Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.
LA - eng
KW - generalized absolute continuity; Henstock-Kurzweil integral; generalized absolute continuity; Henstock-Kurzweil integral
UR - http://eudml.org/doc/30973
ER -

References

top
  1. Real Analysis, Prentice-Hall, , 1997. (1997) 
  2. 10.1090/S0002-9939-1991-1034883-6, Proc. American Math. Soc. 111 (1991), 127–129. (1991) Zbl0732.26011MR1034883DOI10.1090/S0002-9939-1991-1034883-6
  3. A descriptive definition of some multidimensional gauge integrals, Czechoslovak Math.  J. 45 (1995), 549–562. (1995) MR1344520
  4. The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics Vol. 4, AMS, Providence, 1994. (1994) MR1288751
  5. Perron-type integration on n -dimensional intervals and its properties, Czechoslovak Math. J. 45 (1995), 79–106. (1995) MR1314532
  6. 10.4153/CJM-1991-032-8, Canad.  J. Math. 43 (1991), 526–539. (1991) MR1118008DOI10.4153/CJM-1991-032-8
  7. Equiintegrability and controlled convergence of Perron-type integrable functions, Real Anal. Exchange 17 (1991/92), 110–139. (1991/92) MR1147361
  8. 10.1007/BF03323075, Results Math. 21 (1992), 138–151. (1992) MR1146639DOI10.1007/BF03323075
  9. The Radon-Nikodým theorem for the Henstock integral in Euclidean space, Real Anal. Exchange 22 (1996/97), 677–687. (1996/97) MR1460980
  10. The integral, an easy approach after Kurzweil and Henstock, Australian Mathematical Society Lecture Series  14, Cambridge University Press, Cambridge, 2000. (2000) MR1756319
  11. On Henstock integrability in Euclidean spaces, Real Anal. Exchange 22 (1996/97), 382–389. (1996/97) MR1433623
  12. 10.1007/s10587-004-6415-7, Czechoslovak Math.  J. 54 (2004), 657–674. (2004) MR2086723DOI10.1007/s10587-004-6415-7
  13. The sharp Riesz-type definition for the Henstock-Kurzweil integral, Real Anal. Exchange 28 (2002/2003), 55–70. (2002/2003) MR1973968
  14. A full descriptive definition of the Henstock-Kurzweil integral in the Euclidean space, Proc. London Math. Soc. 87 (2003), 677–700. (2003) Zbl1047.26006MR2005879
  15. Some full characterizations of the strong McShane integral, Math. Bohem. 129 (2004), 305–312. (2004) Zbl1080.26006MR2092716
  16. 10.1112/S0024609398005347, Bull. London Math. Soc. 31 (1999), 173–180. (1999) MR1664188DOI10.1112/S0024609398005347
  17. Theory of the Integral, 2nd edition, Stechert & Co., New York, 1964. (1964) MR0167578

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.