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 ?
Then, by the Lemma, Lebesgue dominated convergence theorem, and Fubini's theorem,
Let u = x - t + y/2 and v = x - y/2 in the last term, by Lemma, Fubini's Theorem and the Lebesgue dominated convergence theorem,
Hence, using Fubini's theorem and the first point of Proposition 10,
For the first expectation, by Fubini's theorem we have
1) and Fubini's theorem we have for almost every y [member of] I[R.
Then, the Fubini's theorem implies that we can exchange the order of the sum and the q-integral signs, and we obtain
Using Fubini's theorem we can rewrite the right-hand side of Eq.
Since [0, +[infinity][x{0} and {0} x [0,+[infinity][ are [mu]-nulls, by Fubini's theorem and a change of variable we obtain
Hence, using the Fubini's theorem and the properties of the generalized q-Dunkl translation, we get
So, by the Fubini's theorem, we can exchange the order of the q-integrals and obtain,