• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.543-550
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• 2007

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].