Some comments on an approximately continuous Khintchine integral
The author defines the \(AK_N\) integral and shows that it includes the general Denjoy (Khintchine) integral, the approximately continuous integral of Burkill, and the Kubota integral. A function \(f\) is \(AK_N\) integrable on \([a, b]\) if there is an approximately continuous function \(F\) which is BVG and satisfies Lusin's condition such that the approximate derivative \(F_{ap}'= f\) almost everywhere in \([a, b]\). For a Riemann-type definition of the Kubota integral, see \textit{T.-Y. Lee} and \textit{P.-Y. Lee} [Math. Jap. 42, No. 2, 257-263 (1995; Zbl 0844.26006)].
approximately continuous integral of Burkill
scientific article; zbMATH DE number 801041