Two types of absolute continuity used in Henstock and AP integration are equivalent (Q1322629)

It is known that the primitive of an AP integrable function is \((\delta)\text{ACG}^*_{ap}\) as well as \(\text{ACG}^{**}_{ap}\) in which the former involves one partition whereas the latter two partitions. The author shows that the two are equivalent. Similarly, the same holds for the Henstock integral on the real line. For definition of AP and Henstock, see the reviewer: ``Lanzhou lectures on Henstock integration'' (1989; Zbl 0699.26004).