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Denjoy Integral

A type of Integral which is an extension of both the Riemann Integral and the Lebesgue Integral. The original Denjoy integral is now called a Denjoy integral ``in the restricted sense,'' and a more general type is now called a Denjoy integral ``in the wider sense.'' The independently discovered Peron Integral turns out to be equivalent to the Denjoy integral ``in the restricted sense.''

See also Integral, Lebesgue Integral, Peron Integral, Riemann Integral


Iyanaga, S. and Kawada, Y. (Eds.). ``Denjoy Integrals.'' §103 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 337-340, 1980.

Kestelman, H. ``General Denjoy Integral.'' §9.2 in Modern Theories of Integration, 2nd rev. ed. New York: Dover, pp. 217-227, 1960.

© 1996-9 Eric W. Weisstein