# Khinchin integral

From Encyclopedia of Mathematics

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) |

**How to Cite This Entry:**

Khinchin integral.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Khinchin_integral&oldid=32527

This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article