• Park, Jae-Myung ;
  • Kim, Young-Kuk ;
  • Yoon, Ju-Ran
  • Published : 2005.08.01


In this paper, we define the ap-Denjoy integral and investigate some properties of the ap-Denjoy integral.


ap-Denjoy integral;approximate Lusin function;approximately differentiable


  1. T. S. Chew and Kecheng Liao, The descriptive definitions and properties of the AP-integral and their application to the problem of controlled convergence, Real Anal. Exchange 19 (1993-1994), 81-97
  2. P. S. Bullen, The Burkill approximately continuous integral, J. Aust. Math. Soc. (Series A) 35 (1983), 236-253
  3. R. A. Gordon, Some comments on the McShane and Henstock integrals, Real Anal. Exchange 23 (1997-1998), 329-342
  4. R. A. Gordon, The Integrals of Lebesgue, Denjoy, Perron and Henstock, Amer. Math. Soc. Providence, R.I. 1994
  5. J. Kurzweil, On multiplication of Perron integrable functions, Czechoslovak Math. J. 23 (1973), no. 98, 542-566
  6. J. Kurzweil and J. Jarnik, Perron type integration on n-dimensional inter- vals as an extension of integration of step functions by strong equiconvergence, Czechoslovak Math. J. 46 (1996), no. 121, 1-20
  7. T. Y. Lee, On a generalized dominated convergence theorem for the AP integral, Real Anal. Exchange 20 (1994-1995), 77-88
  8. K. Liao, On the descriptive definition of the Burkill approximately continuous integral, Real Anal. Exchange 18 (1992-1993), 253-260
  9. Y. J. Lin, On the equivalence of four convergence theorems for the AP-integral, Real Anal. Exchange 19 (1993-1994), 155-164
  10. J. M. Park, Bounded convergence theorem and integral operator for operator valued measures, Czechoslovak Math. J. 47 (1997), no. 122, 425-430
  11. J. M. Park, The Denjoy extension of the Riemann and McShane integrals, Czechoslovak Math. J. 50 (2000), no. 125, 615-625
  12. J. M. Park, C. G. Park, J. B. Kim, D. H. Lee and W. Y. Lee, The integrals of s-Perron, sap-Perron and ap-McShane, Czechoslovak Math. J. 54 (2004), no. 129, 545-557
  13. A.M. Russell, A Banach space of functions of generalized variation, Bull. Austral. Math. Soc. 15 (1976), 431-438
  14. A.M. Russell, Stieltjes type integrals, J. Aust. Math. Soc. (Series A) 20 (1975), 431-448

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