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.
|||A.Ya. Khinchin, "Sur une extension de l'intégrale de M. Denjoy" C.R. Acad. Sci. Paris , 162 (1916) pp. 287–291|
|||A.Ya. Khinchin, Mat. Sb. , 30 (1918) pp. 543–557|
|||I.N. Pesin, "Classical and modern integration theories" , Acad. Press (1970) (Translated from Russian)|
|||S. Saks, "Theory of the integral" , Hafner (1952) (Translated from French)|
Khinchin integral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Khinchin_integral&oldid=32527