Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A NOTE ON THE AP-DENJOY INTEGRAL

  • Park, Jae Myung (Department of Mathematics Chungnam National University) ;
  • Kim, Byung Moo (Department of General Arts Chungju National University) ;
  • Kim, Young Kuk (Department of Mathematics Education Seowon University)
  • Received : 2007.11.07
  • Published : 2007.12.31
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Abstract

In this paper, we define the ap-Denjoy integral and investigate some properties od the ap-Denjoy integral. In particular, we show that a function f : [a,b]${\rightarrow}\mathbb{R}$ is ap-Denjoy integrable on [a,b] if and only if there exists an $ACG_s$ function F on [a,b] such that $F^{\prime}_{ap}=f$ almost everywhere on [a,b].

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