The s-Perron, sap-Perron and ap-McShane integrals

Joo Bong Kim; Deok Ho Lee; Woo Youl Lee; Chun-Gil Park; Jae Myung Park

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 3, page 545-557
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Kim, Joo Bong, et al. "The s-Perron, sap-Perron and ap-McShane integrals." Czechoslovak Mathematical Journal 54.3 (2004): 545-557. <http://eudml.org/doc/30881>.

@article{Kim2004,
abstract = {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.},
author = {Kim, Joo Bong, Lee, Deok Ho, Lee, Woo Youl, Park, Chun-Gil, Park, Jae Myung},
journal = {Czechoslovak Mathematical Journal},
keywords = {s-Perron integral; sap-Perron integral; ap-McShane integral; s-Perron integral; sap-Perron integral; ap-McShane integral},
language = {eng},
number = {3},
pages = {545-557},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The s-Perron, sap-Perron and ap-McShane integrals},
url = {http://eudml.org/doc/30881},
volume = {54},
year = {2004},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 3
SP - 545
EP - 557
AB - 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.
LA - eng
KW - s-Perron integral; sap-Perron integral; ap-McShane integral; s-Perron integral; sap-Perron integral; ap-McShane integral
UR - http://eudml.org/doc/30881
ER -

References

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  1. 10.1017/S1446788700025738, J.  Austral. Math. Soc. Ser.  A 35 (1983), 236–253). (1983) Zbl0533.26006MR0704431DOI10.1017/S1446788700025738
  2. 10.2307/44153816, Real Analysis Exchange 19 (1993-1994), 81–97. (1993-1994) MR1268833DOI10.2307/44153816
  3. 10.2307/44152859, Real Analysis Exchange 23 (1997–1998), 329–342. (1997–1998) MR1609917DOI10.2307/44152859
  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 Analysis Exchange 20 (1994–1995), 77–88. (1994–1995) MR1313672
  8. 10.2307/44133066, Real Analysis Exchange 18 (1992–1993), 253–260. (1992–1993) MR1205520DOI10.2307/44133066
  9. 10.2307/44153824, Real Analysis Exchange 19 (1993–1994), 155–164. (1993–1994) MR1268841DOI10.2307/44153824
  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. 10.1017/S1446788700016153, J.  Austral. Math. Soc. Ser.  A 20 (1975), 431–448. (1975) Zbl0313.26012MR0393379DOI10.1017/S1446788700016153
  13. 10.1017/S0004972700022863, Bull. Austral. Math. Soc. 15 (1976), 431–438. (1976) Zbl0333.46025MR0430180DOI10.1017/S0004972700022863

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