Geodesic
The s-Perron, sap-Perron and ap-McShane integrals
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 545-557
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we study the s-Perron, sap-Perron and ap-McShane integrals. In particular, we show that the s-Perron integral is equivalent to the McShane integral and that the sap-Perron integral is equivalent to the ap-McShane integral.
In this paper, we study the s-Perron, sap-Perron and ap-McShane integrals. In particular, we show that the s-Perron integral is equivalent to the McShane integral and that the sap-Perron integral is equivalent to the ap-McShane integral.
Classification : 26A39, 28B05
Keywords: s-Perron integral; sap-Perron integral; ap-McShane integral 
@article{CMJ_2004_54_3_a0,
     author = {Kim, Joo Bong and Lee, Deok Ho and Lee, Woo Youl and Park, Chun-Gil and Park, Jae Myung},
     title = {The {s-Perron,} {sap-Perron} and {ap-McShane} integrals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {545--557},
     year = {2004},
     volume = {54},
     number = {3},
     mrnumber = {2086715},
     zbl = {1080.26005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a0/}
}
TY  - JOUR
AU  - Kim, Joo Bong
AU  - Lee, Deok Ho
AU  - Lee, Woo Youl
AU  - Park, Chun-Gil
AU  - Park, Jae Myung
TI  - The s-Perron, sap-Perron and ap-McShane integrals
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 545
EP  - 557
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a0/
LA  - en
ID  - CMJ_2004_54_3_a0
ER  - 
%0 Journal Article
%A Kim, Joo Bong
%A Lee, Deok Ho
%A Lee, Woo Youl
%A Park, Chun-Gil
%A Park, Jae Myung
%T The s-Perron, sap-Perron and ap-McShane integrals
%J Czechoslovak Mathematical Journal
%D 2004
%P 545-557
%V 54
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a0/
%G en
%F CMJ_2004_54_3_a0
Kim, Joo Bong; Lee, Deok Ho; Lee, Woo Youl; Park, Chun-Gil; Park, Jae Myung. The s-Perron, sap-Perron and ap-McShane integrals. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 545-557. http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a0/

[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, and K.  Liao: The descriptive definitions and properties of the AP-integral and their application to the problem of controlled convergence. Real Analysis Exchange 19 (1993-1994), 81–97. | DOI | MR

[3] R. A.  Gordon: Some comments on the McShane and Henstock integrals. Real Analysis Exchange 23 (1997–1998), 329–342. | DOI | MR

[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, and 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 Analysis Exchange 20 (1994–1995), 77–88. | MR

[8] K.  Liao: On the descriptive definition of the Burkill approximately continuous integral. Real Analysis Exchange 18 (1992–1993), 253–260. | DOI | MR

[9] Y. J.  Lin: On the equivalence of four convergence theorems for the AP-integral. Real Analysis Exchange 19 (1993–1994), 155–164. | DOI | MR

[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] A. M.  Russell: Stieltjes type integrals. J.  Austral. Math. Soc. Ser.  A 20 (1975), 431–448. | DOI | MR | Zbl

[13] A. M.  Russell: A Banach space of functions of generalized variation. Bull. Austral. Math. Soc. 15 (1976), 431–438. | DOI | MR | Zbl