View source for Khinchin integral

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

A function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055380/k0553801.png" /> is said to be integrable in the sense of Khinchin on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055380/k0553802.png" /> 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====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.Ya. Khinchin,   "Sur une extension de l'intégrale de M. Denjoy"  ''C.R. Acad. Sci. Paris'' , '''162'''  (1916)  pp. 287–291</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  A.Ya. Khinchin,   ''Mat. Sb.'' , '''30'''  (1918)  pp. 543–557</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  I.N. Pesin,   "Classical and modern integration theories" , Acad. Press  (1970)  (Translated from Russian)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top">  S. Saks,   "Theory of the integral" , Hafner  (1952)  (Translated from French)</TD></TR></table>