Transcription of Fubini's theorem
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Fubini's theorem
Fubini's theorem1 Fubini's theoremIn mathematical analysis Fubini's theorem , named after Guido Fubini, is a result which gives conditions underwhich it is possible to compute a double integral using iterated integrals. As a consequence it allows the order ofintegration to be changed in iterated statementSuppose A and B are complete measure spaces. Suppose f(x,y) is A B measurable. Ifwhere the integral is taken with respect to a product measure on the space over A B, thenthe first two integrals being iterated integrals with respect to two measures, respectively, and the third being anintegral with respect to a product of these two the above integral of the absolute value is not finite, then the two iterated integrals may actually have differentvalues. See below for an illustration of this f(x,y) = g(x)h(y) for some functions g and h, thenthe integral on the right side being with respect to a product theorem statementAnother version of Fubini's theorem states that if A and B are -finite measure spaces, not necessarily complete, andif either or this version the condition that the measures are -finite is 's theorem2 Tonelli's theoremTonelli's theorem (named after Leonida Tonelli) is a successor of Fubini's theor
Fubini's theorem 1 Fubini's theorem In mathematical analysis Fubini's theorem, named after Guido Fubini, is a result which gives conditions under which it is possible to compute a double integral using iterated integrals. As a consequence it allows the order of
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