Fubini's theorem

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Fubini's theorem

[fü′bē·nēz ‚thir·əm]
(mathematics)
The theorem stating conditions under which
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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We have from an application of the Fubini theorem that (47) generalizes the classical Fourier transform.
For x [member of] [L.sub.p]([R.sup.+], X), by Fubini Theorem and condition (b) of Theorem 2.1 of [15], we obtain
Setting u = [e.sup.ax+by] in (10), in view of Fubini theorem (cf.
For [[sigma].sub.1] = [sigma], by Fubini theorem (see [24]) and (29), we have
Making use of the Fubini theorem and a substitution technique, we have
If, in addition, dimX < [infinity], then a classical Fubini theorem allows one to conclude that Z is of Lebesgue measure zero.
The proof is a simple application of the Fubini theorem as follows:
In view of the Fubini theorem, we have [J.sub.1] = [K.sub.1].
The techniques are a melange of Fubini theorem, an elementary version of resolution of singularities and some fairly standard results from the theory of generalized functions.
by the Fubini theorem and the change of variable theorem, which proves (60).
According to the law of iterated expectations and Fubini theorem we have