The ap-Denjoy and ap-Henstock integrals

Jae Myung Park; Jae Jung Oh; Chun-Gil Park; Deuk Ho Lee

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 2, page 689-696
  • ISSN: 0011-4642

Abstract

top
In this paper we define the ap-Denjoy integral and show that the ap-Denjoy integral is equivalent to the ap-Henstock integral and the integrals are equal.

How to cite

top

Park, Jae Myung, et al. "The ap-Denjoy and ap-Henstock integrals." Czechoslovak Mathematical Journal 57.2 (2007): 689-696. <http://eudml.org/doc/31155>.

@article{Park2007,
abstract = {In this paper we define the ap-Denjoy integral and show that the ap-Denjoy integral is equivalent to the ap-Henstock integral and the integrals are equal.},
author = {Park, Jae Myung, Oh, Jae Jung, Park, Chun-Gil, Lee, Deuk Ho},
journal = {Czechoslovak Mathematical Journal},
keywords = {approximate Lusin function; ap-Denjoy integral; ap-Henstock integral; choice; approximate Lusin function; ap-Denjoy integral; ap-Henstock integral; choice},
language = {eng},
number = {2},
pages = {689-696},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The ap-Denjoy and ap-Henstock integrals},
url = {http://eudml.org/doc/31155},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Park, Jae Myung
AU - Oh, Jae Jung
AU - Park, Chun-Gil
AU - Lee, Deuk Ho
TI - The ap-Denjoy and ap-Henstock integrals
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 689
EP - 696
AB - In this paper we define the ap-Denjoy integral and show that the ap-Denjoy integral is equivalent to the ap-Henstock integral and the integrals are equal.
LA - eng
KW - approximate Lusin function; ap-Denjoy integral; ap-Henstock integral; choice; approximate Lusin function; ap-Denjoy integral; ap-Henstock integral; choice
UR - http://eudml.org/doc/31155
ER -

References

top
  1. 10.1017/S1446788700025738, J.  Austral. Math. Soc. (Ser.  A) 35 (1983), 236–253. (1983) Zbl0533.26006MR0704431DOI10.1017/S1446788700025738
  2. The descriptive definitions and properties of the AP-integral and their application to the problem of controlled convergence, Real Anal. Exch. 19 (1994), 81–97. (1994) MR1268833
  3. 10.2307/44152859, Real Anal. Exch. 23 (1997), 329–341. (1997) Zbl0943.26023MR1609917DOI10.2307/44152859
  4. The Integrals of Lebesgue, Denjoy, Perron and Henstock, Amer. Math. Soc., Providence, 1994. (1994) Zbl0807.26004MR1288751
  5. On multiplication of Perron integrable functions, Czechoslovak Math.  J. 23(98) (1973), 542–566. (1973) Zbl0269.26007MR0335705
  6. Perron type integration on n-dimensional intervals as an extension of integration of step functions by strong equiconvergence, Czechoslovak Math.  J. 46(121) (1996), 1–20. (1996) MR1371683
  7. On a generalized dominated convergence theorem for the AP  integral, Real Anal. Exch. 20 (1995), 77–88. (1995) Zbl0820.26006MR1313672
  8. 10.2307/44133066, Real Anal. Exch. 18 (1993), 253–260. (1993) Zbl0774.26006MR1205520DOI10.2307/44133066
  9. On the equivalence of four convergence theorems for the AP-integral, Real Anal. Exch. 19 (1994), 155–164. (1994) Zbl0813.26002MR1268841
  10. 10.1023/A:1022403232211, Czechoslovak Math.  J. 47(122) (1997), 425–430. (1997) Zbl0903.46040MR1461422DOI10.1023/A:1022403232211
  11. 10.1023/A:1022845929564, Czechoslovak Math.  J. 50(125) (2000), 615–625. (2000) Zbl1079.28502MR1777481DOI10.1023/A:1022845929564
  12. 10.1007/s10587-004-6407-7, Czechoslovak Math.  J. 54(129) (2004), 545–557. (2004) MR2086715DOI10.1007/s10587-004-6407-7
  13. 10.1017/S1446788700016153, J.  Austr. Math. Soc. (Ser.  A) 20 (1975), 431–448. (1975) Zbl0313.26012MR0393379DOI10.1017/S1446788700016153
  14. 10.1017/S0004972700022863, Bull. Aust. Math. Soc. 15 (1976), 431–438. (1976) Zbl0333.46025MR0430180DOI10.1017/S0004972700022863

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.