| Title:
|
The ap-Denjoy and ap-Henstock integrals (English) |
| Author:
|
Park, Jae Myung |
| Author:
|
Oh, Jae Jung |
| Author:
|
Park, Chun-Gil |
| Author:
|
Lee, Deuk Ho |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
689-696 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
approximate Lusin function |
| Keyword:
|
ap-Denjoy integral |
| Keyword:
|
ap-Henstock integral |
| Keyword:
|
choice |
| MSC:
|
26A39 |
| MSC:
|
28B05 |
| idZBL:
|
Zbl 1174.26308 |
| idMR:
|
MR2337623 |
| . |
| Date available:
|
2009-09-24T11:48:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128198 |
| . |
| Reference:
|
[1] P. S. Bullen: The Burkill approximately continuous integral.J. Austral. Math. Soc. (Ser. A) 35 (1983), 236–253. Zbl 0533.26006, MR 0704431, 10.1017/S1446788700025738 |
| Reference:
|
[2] T. S. Chew, K. Liao: 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. MR 1268833 |
| Reference:
|
[3] R. A. Gordon: Some comments on the McShane and Henstock integrals.Real Anal. Exch. 23 (1997), 329–341. Zbl 0943.26023, MR 1609917, 10.2307/44152859 |
| Reference:
|
[4] R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron and Henstock.Amer. Math. Soc., Providence, 1994. Zbl 0807.26004, MR 1288751 |
| Reference:
|
[5] J. Kurzweil: On multiplication of Perron integrable functions.Czechoslovak Math. J. 23(98) (1973), 542–566. Zbl 0269.26007, MR 0335705 |
| Reference:
|
[6] J. Kurzweil, J. Jarník: 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. MR 1371683 |
| Reference:
|
[7] T. Y. Lee: On a generalized dominated convergence theorem for the AP integral.Real Anal. Exch. 20 (1995), 77–88. Zbl 0820.26006, MR 1313672 |
| Reference:
|
[8] K. Liao: On the descriptive definition of the Burkill approximately continuous integral.Real Anal. Exch. 18 (1993), 253–260. Zbl 0774.26006, MR 1205520, 10.2307/44133066 |
| Reference:
|
[9] Y. J. Lin: On the equivalence of four convergence theorems for the AP-integral.Real Anal. Exch. 19 (1994), 155–164. Zbl 0813.26002, MR 1268841 |
| Reference:
|
[10] J. M. Park: Bounded convergence theorem and integral operator for operator valued measures.Czechoslovak Math. J. 47(122) (1997), 425–430. Zbl 0903.46040, MR 1461422, 10.1023/A:1022403232211 |
| Reference:
|
[11] J. M. Park: The Denjoy extension of the Riemann and McShane integrals.Czechoslovak Math. J. 50(125) (2000), 615–625. Zbl 1079.28502, MR 1777481, 10.1023/A:1022845929564 |
| Reference:
|
[12] J. M. Park, C. G. Park, J. B. Kim, D. H. Lee, and W. Y. Lee: The $s$-Perron, sap-Perron and ap-McShane integrals.Czechoslovak Math. J. 54(129) (2004), 545–557. MR 2086715, 10.1007/s10587-004-6407-7 |
| Reference:
|
[13] A. M. Russell: Stieltjes type integrals.J. Austr. Math. Soc. (Ser. A) 20 (1975), 431–448. Zbl 0313.26012, MR 0393379, 10.1017/S1446788700016153 |
| Reference:
|
[14] A. M. Russell: A Banach space of functions of generalized variation.Bull. Aust. Math. Soc. 15 (1976), 431–438. Zbl 0333.46025, MR 0430180, 10.1017/S0004972700022863 |
| . |
