To my understanding the definition of the McShane integral is identical to the definition of the Henstock–Kurzweil integral with the exception that each tag does not have to be contained in the subinterval for which it is assigned to. However, the gauge function in general will force the corresponding subinterval to be relatively close to the tag. Still, the tag can be picked a bit outside of the subinterval. If I am not mistakes this implies that a function is McShane integrable if and only if it is absolutely integrable. This is not the case for the Henstock–Kurzweil integral. I do not understand how such a subtle modification of the definition of the Henstock–Kurzweil integral makes every McShane integrable function absolutely McShane integrable. By functions I am simply refering to functions on $\mathbb{R}$ for the sake of simplicity. Is there an intuitive way to view the differences between the aforementioned integrals and in particular why McShane integrable functions are absolutely integrable?
2026-03-25 06:30:32.1774420232
Is there an intuitive way to view the definition of the McShane integral?
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