Teorema (de Fubini, cálculo de integrais via integrais iterados.) Seja f:J×K→R uma função limitada integrável no produto cartesiano de intervalos limitados e. Fubini, G. Il teorema di riduzione per gli integrali doppi. Rendiconti del Seminario Matematico dell'Università e del Politecnico di Torino 9: –; Opere. Besides, a Fubini's type theorem is proved for nite radon measures. Finally, we will prove Producto tensorial de medidas radonianas y el teorema de Fubini.


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El teorema de Radon-Nikodym en espacios bornologicos. On integration in Banach spaces III.

IV, 30; ibid. V, 30; ibid. VII, 38 On the projective tensor product of vector-valued measures Teorema de fubini. Inductive tensor product of vector valued measures.

A counter-example on the inner product of measures.

Cálculo de integrais em limitados de $\mathbb{R}^n$ via integrais iterados

Counterexamples[ edit ] The following examples show how Fubini's theorem and Tonelli's theorem can fail if any of their teorema de fubini are omitted.

So the two iterated integrals are different. In the example above, for the maximal product measure, the diagonal has infinite measure so the double integral of f is infinite, and Fubini's theorem holds vacuously.


This gives an example of a product measure where Fubini's theorem fails. This gives an example of two different product measures teorema de fubini the same product of two measure spaces. Failure of Tonelli's theorem for non-measurable functions[ edit ] Suppose that X is the first uncountable ordinal, with the finite measure where the measurable sets are either countable with measure 0 teorema de fubini the sets of countable complement with measure 1.

If f is the characteristic function of E then the two iterated integrals of f are defined and have different values 1 and 0. The function f is not measurable. This shows that Tonelli's theorem can fail for non-measurable functions.

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