Fubini's theorem


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Fubini's theorem

[fü′bē·nēz ‚thir·əm]
(mathematics)
The theorem stating conditions under which
References in periodicals archive ?
Together with (3.5) in [1], Fubini's theorem, and the reproducing property, we can see that
By law of total expectation and Fubini's theorem, we have
Combining (2.18)-(2.19) and Fubini's theorem, when [x.sub.1] [conjunction] [x.sub.2] [greater than or equal to] [x'.sub.3] and t > 0, we have
Making the change of variables y = x + [tau]/2 and z = x - [tau]/2 and applying Fubini's theorem we obtain
Using the assumption that the QFT of quaternion mother wavelet is real-valued and then applying Fubini's theorem, we obtain
Applying change of variables and Fubini's theorem, we can derive the following four estimates:
Then, by the Lemma, Lebesgue dominated convergence theorem, and Fubini's theorem,
Hence, using Fubini's theorem and the first point of Proposition 10,
since E [[integral].sup.t.sub.0] B[(t).sup.4] dt = [[integral].sup.T.sub.0] E[B[(t).sup.4]] dt by Fubini's theorem and E[B[(t).sup.4]] = 3[t.sup.2].
From the relation (4.1) and Fubini's theorem we have for almost every y [member of] I[R.sup.d]: