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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 Perron integral turns out to be equivalent to the Denjoy integral "in the restricted sense."


See also

Integral, Lebesgue Integral, Perron Integral, Riemann Integral

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References

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.

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Denjoy Integral

Cite this as:

Weisstein, Eric W. "Denjoy Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DenjoyIntegral.html

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