Khinchin integral

A generalization of the narrow Denjoy integral introduced by A.Ya. Khinchin in [1].

A function $f$ is said to be integrable in the sense of Khinchin on $[a,b]$ if it is Denjoy-integrable in the wide sense and if its indefinite integral is differentiable almost everywhere. Sometimes the Khinchin integral is also called the Denjoy–Khinchin integral.

References

[1]	A.Ya. Khinchin, "Sur une extension de l'intégrale de M. Denjoy" C.R. Acad. Sci. Paris , 162 (1916) pp. 287–291
[2]	A.Ya. Khinchin, Mat. Sb. , 30 (1918) pp. 543–557
[3]	I.N. Pesin, "Classical and modern integration theories" , Acad. Press (1970) (Translated from Russian)
[4]	S. Saks, "Theory of the integral" , Hafner (1952) (Translated from French)