Product measures

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On the Cartesian product of two measure spaces one can construct a measure—hence, an integral—which is directly connected with the measure on each factor. Then, the natural problem that arises is how to reduce a double (or multiple) integral to the computation of two (or more) simple integrals. Such a question plays a crucial role in Lebesgue integration.

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Cannarsa, P., & D’Aprile, T. (2015). Product measures. In UNITEXT - La Matematica per il 3 piu 2 (Vol. 89, pp. 107–130). Springer-Verlag Italia s.r.l.

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