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Fubini Theorem

Fubini's theorem, sometimes called Tonelli's theorem, establishes a connection between a multiple integral and a repeated one. If f(x,y) is continuous on the rectangular region R:a<=x<=b,c<=y<=d, then the equality

intint_Rf(x,y)d(x,y)=int_a^bint_c^df(x,y)dydx

holds (Thomas and Finney 1996, p. 919).

See also

Definite Integral, Multiple Integral, Repeated Integral

Portions of this entry contributed by Ronald M. Aarts

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References

Borwein, J.; Bailey, D.; and Girgensohn, R. Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters, p. 18, 2004.Fubine, G. "Sugli integrali multipli." Opere scelte, Vol. 2. Cremonese, pp. 243-249, 1958.Samko, S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional Integrals and Derivatives. Yverdon, Switzerland: Gordon and Breach, p. 9, 1993.Thomas, G. B., Jr. and Finney, R. L. Calculus and Analytic Geometry, 8th ed. Reading, MA: Addison-Wesley, p. 919, 1996.

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Fubini Theorem

Cite this as:

Weisstein, Eric W., with contributions by Ronald M. Aarts. "Fubini Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FubiniTheorem.html

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