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We locate Musial and Sagher's concept of -integration within the approximate Henstock–Kurzweil integral theory. If we restrict the -integral by the requirement that the indefinite -integral is continuous, then it becomes included in the classical Denjoy–Khintchine integral. We provide a direct argument demonstrating that this inclusion is proper. [ABSTRACT FROM AUTHOR]

We compare a Perron-type integral with a Henstock-Kurzweil-type integral, both having been introduced to recover functions from their generalized derivatives defined in the metric L^r. We give an example of an HK_r-integrable function which is not P_r-integrable, thereby showing that the first integral is strictly wider than the second one. [ABSTRACT FROM AUTHOR]