Difference between revisions of "Khinchin integral"
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A generalization of the narrow [[Denjoy integral|Denjoy integral]] introduced by A.Ya. Khinchin in [[#References|[1]]]. | A generalization of the narrow [[Denjoy integral|Denjoy integral]] introduced by A.Ya. Khinchin in [[#References|[1]]]. | ||
| − | A function | + | 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==== | ====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> | <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> | ||
Latest revision as of 08:39, 23 July 2014
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=11941
Khinchin integral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Khinchin_integral&oldid=11941
This article was adapted from an original article by T.P. Lukashenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article