Keywords: approximate Lusin function; ap-Denjoy integral; ap-Henstock integral; choice
@article{CMJ_2007_57_2_a11,
author = {Park, Jae Myung and Oh, Jae Jung and Park, Chun-Gil and Lee, Deuk Ho},
title = {The {ap-Denjoy} and {ap-Henstock} integrals},
journal = {Czechoslovak Mathematical Journal},
pages = {689--696},
year = {2007},
volume = {57},
number = {2},
mrnumber = {2337623},
zbl = {1174.26308},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a11/}
}
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 SP - 689 EP - 696 VL - 57 IS - 2 UR - http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a11/ LA - en ID - CMJ_2007_57_2_a11 ER -
Park, Jae Myung; Oh, Jae Jung; Park, Chun-Gil; Lee, Deuk Ho. The ap-Denjoy and ap-Henstock integrals. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 689-696. http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a11/
[1] P. S. Bullen: The Burkill approximately continuous integral. J. Austral. Math. Soc. (Ser. A) 35 (1983), 236–253. | DOI | MR | Zbl
[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
[3] R. A. Gordon: Some comments on the McShane and Henstock integrals. Real Anal. Exch. 23 (1997), 329–341. | DOI | MR | Zbl
[4] R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron and Henstock. Amer. Math. Soc., Providence, 1994. | MR | Zbl
[5] J. Kurzweil: On multiplication of Perron integrable functions. Czechoslovak Math. J. 23(98) (1973), 542–566. | MR | Zbl
[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
[7] T. Y. Lee: On a generalized dominated convergence theorem for the AP integral. Real Anal. Exch. 20 (1995), 77–88. | MR | Zbl
[8] K. Liao: On the descriptive definition of the Burkill approximately continuous integral. Real Anal. Exch. 18 (1993), 253–260. | DOI | MR | Zbl
[9] Y. J. Lin: On the equivalence of four convergence theorems for the AP-integral. Real Anal. Exch. 19 (1994), 155–164. | MR | Zbl
[10] J. M. Park: Bounded convergence theorem and integral operator for operator valued measures. Czechoslovak Math. J. 47(122) (1997), 425–430. | DOI | MR | Zbl
[11] J. M. Park: The Denjoy extension of the Riemann and McShane integrals. Czechoslovak Math. J. 50(125) (2000), 615–625. | DOI | MR | Zbl
[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. | DOI | MR
[13] A. M. Russell: Stieltjes type integrals. J. Austr. Math. Soc. (Ser. A) 20 (1975), 431–448. | DOI | MR | Zbl
[14] A. M. Russell: A Banach space of functions of generalized variation. Bull. Aust. Math. Soc. 15 (1976), 431–438. | DOI | MR | Zbl