Khinchin integral

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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.


[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)
How to Cite This Entry:
Khinchin integral. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article