On the approximately continuous integrals of Burkill and Kubota (Q1978904)

The author gives new and correct proofs of some earlier results due to \textit{Y.~Kubota} [Proc. Japan Acad. 40, 713-717 (1964; Zbl 0141.24601); ibid. 42, 737-742 (1966; Zbl 0145.05903)]. In particular, he shows that the relation AP \(\subset \) AD = AP\(^*\) is true, where AD stands for the set of functions having approximately continuous Perron integral on \([a,b]\) (in the sense of \textit{J.~Burkill} [Math. Z. 34, 270-278 (1931; Zbl 0002.38604)]), AD and AP\(^*\) are the sets of functions AD- or AP\(^*\)-integrable on \([a,b]\) in the sense of Kubota.