Every G-integrable function is μ_G-measurable when G is nondecreasing, and every bounded G-integrable function is μ_G-measurable for G of bounded variation; this yields a characterization of Lebesgue integrability via the G-integral.
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On measurability of Kurzweil--Stieltjes integrable functions on compact lines
Every G-integrable function is μ_G-measurable when G is nondecreasing, and every bounded G-integrable function is μ_G-measurable for G of bounded variation; this yields a characterization of Lebesgue integrability via the G-integral.