Theorem Statement
Suppose A and B are complete measure spaces. Suppose f(x,y) is A × B measurable. If
where the integral is taken with respect to a product measure on the space over A × B, then
the first two integrals being iterated integrals with respect to two measures, respectively, and the third being an integral with respect to a product of these two measures.
If the above integral of the absolute value is not finite, then the two iterated integrals may actually have different values. See below for an illustration of this possibility.
Read more about this topic: Fubini's Theorem
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