About: Fubini's theorem

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In mathematical analysis Fubini's theorem is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral, introduced by Guido Fubini in 1907. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value. A related theorem is often called Fubini's theorem for infinite series, which states that if is a doubly-indexed sequence of real numbers, and if is absolutely convergent, then

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rdfs:label	Fubini's theorem (en)
rdfs:comment	In mathematical analysis Fubini's theorem is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral, introduced by Guido Fubini in 1907. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value. A related theorem is often called Fubini's theorem for infinite series, which states that if is a doubly-indexed sequence of real numbers, and if is absolutely convergent, then (en)
sameAs	Fubini's theorem Fubini's theorem
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Subject	Articles containing proofs Theorems in calculus Theorems in measure theory
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Fubini's_theorem?oldid=1063648410&ns=0
Wikipage page ID	255245 (xsd:integer)
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Wikipage revision ID	1063648410 (xsd:integer)
Link from a Wikipage to another Wikipage	List of statements independent of ZFC Product (category theory) Product measure Absolute convergence Absolute value Σ-algebra Σ-finite measure Carathéodory's extension theorem Articles containing proofs Theorems in calculus Disintegration theorem Kuratowski–Ulam theorem Leonhard Euler Set theory Zermelo–Fraenkel set theory Decomposable measure Complete measure Counting measure Order of integration (calculus) Symmetry of second derivatives Guido Fubini Iterated integral Lebesgue integration Lebesgue measure Leonida Tonelli Martin's axiom Numerical analysis Meagre set Measurable function Measure space Multiple integral Riemann integral Theorems in measure theory
has abstract	In mathematical analysis Fubini's theorem is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral, introduced by Guido Fubini in 1907. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value. As a consequence, it allows the order of integration to be changed in certain iterated integrals.Fubini's theorem implies that two iterated integrals are equal to the corresponding double integral across its integrands. Tonelli's theorem, introduced by Leonida Tonelli in 1909, is similar, but applies to a non-negative measurable function rather than one integrable over their domains. A related theorem is often called Fubini's theorem for infinite series, which states that if is a doubly-indexed sequence of real numbers, and if is absolutely convergent, then Although Fubini's theorem for infinite series is a special case of the more general Fubini's theorem, it is not appropriate to characterize it as a logical consequence of Fubini's theorem. This is because some properties of measures, in particular sub-additivity, are often proved using Fubini's theorem for infinite series. In this case, Fubini's general theorem is a logical consequence of Fubini's theorem for infinite series. (en)
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is Wikipage redirect of	An elegant rearrangement of a conditionally convergent iterated integral Fubini's Theorem Fubini-Tonelli Fubini-Tonelli theorem Fubini–Tonelli theorem Fubini's theorem/Examples Fubini's theorem for the Lebesgue integral Fubini Theorem Fubini theorem Fubinis' Theorem Fubinis Theorem Examples of Fubini's theorem A counterexample related to Fubini's theorem
is Link from a Wikipage to another Wikipage of	Fourier inversion theorem List of statements independent of ZFC List of theorems Loewner's torus inequality Null set Numerical integration Abel transform An elegant rearrangement of a conditionally convergent iterated integral Anatole Katok Area of a circle Borel right process Monotone class theorem Morera's theorem Calculus on Manifolds (book) Campbell's theorem (probability) Carathéodory's extension theorem Cavalieri's principle Geometric measure theory Differential form Dirac delta function Distribution (mathematics) Kuratowski–Ulam theorem Leibniz integral rule Decomposable measure Hölder's inequality List of Italian inventions and discoveries List of Italian scientists List of eponyms (A–K) List of integration and measure theory topics

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