On the Relation between Denjoy–Khintchine and \( \operatorname{HK}_{r} \)-Integrals

We locate Musial and Sagher’s concept of $ \operatorname{HK}_{r} $ -integration within the approximate Henstock–Kurzweil integral theory.If we restrict the $ \operatorname{HK}_{r} $ -integral by the requirement that the indefinite $ \operatorname{HK}_{r} $ -integral is continuous,then it becomes included in the classical Denjoy–Khintchine integral.We provide a direct argument demonstrating that this inclusion is proper.