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  "body": "\n## Summary\n\nThe Khinchin integral is an integral on an interval defined through primitives rather than through sums.\nIt is also called the Denjoy–Khinchin integral or the wide Denjoy integral.\nA function is Khinchin integrable when it is, almost everywhere, the [[approximate derivative|4W31MKE01V]] of a continuous function that is generalized [[absolutely continuous|ZT6F4C2YHK]].\nIt extends the [[Henstock–Kurzweil integral|FCGHXDGVV9]], and hence the [[Lebesgue integral|DWJF7ABPR1]] and the [[Perron integral|M077AXJACA]].\n\n## Explanations\n\n### L1 human\n\nIn Lebesgue's theory, the indefinite integrals are exactly the absolutely continuous functions, and each one has the integrand as its derivative almost everywhere.\nThe Khinchin integral relaxes this in two ways.\nThe primitive only has to be absolutely continuous on each of countably many pieces of the interval.\nIt only has to have the function as an approximate derivative, a derivative that may ignore thin sets of points.\nThe integral of $f$ is then the change of the primitive from one end of the interval to the other.\n",
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