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I recently stumbled upon Lebesgue’s criterion for Riemann integrability. It didn't take very long until I found this result quite intuitive. I then began studying the Henstock–Kurzweil integral. Very quickly I realized that finding the necessary and sufficient conditions for a function to be Henstock–Kurzweil integrable would be much more difficult since functions with significantly worse discontinuities have to be treated. Has there been any research on this topic?

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