Uniform Kurzweil-Henstock integrability (Q1322625)

The author phrased the Kurzweil-Henstock integral in terms of summands (Riemann sums) and differentials (equivalence classes of summands) as in earlier papers [see, for example, the author, Real Anal. Exch. 12(1986/87), 144-175 (1987; Zbl 0638.26009)]. Then the author proved among others a theorem which gives ten different conditions (some newly formulated) each of which is equivalent to the uniform integrability of the summands \(f_ n \Delta x\) for \(n=1,2,\dots\) . For the Kurzweil- Henstock integral, see, for example, the reviewer: ``Lanzhou lectures on Henstock integration'' (1989; Zbl 0699.26004).