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In mathematics, the Henstock-Kurzweil integral is a possible definition of the integral of a function. In the same way that the Lebesgue integral generalizes the Riemann integral, it generalizes the Lebesgue integral. It does so without requiring the use of theorems from measure theory. Instead, the definition of the HK integral is similar to that of the Riemann integral.
This integral first appeared in forms described by Denjoy and by Perron. These turned out to be equivalent, but the formulations have been found opaque. Later Henstock and Kurzweil simplified the description of this integral and invented the Gauge integral. Some educators advocate that this integral should replace the Riemann integral in introductory calculus courses.
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