Fubini's Theorem states that for a measurable function defined on a product measure space, the double integral of that function can be computed as an iterated integral. This theorem is crucial for switching the order of integration in multiple integrals, allowing us to integrate first with respect to one variable and then with respect to another. Its application simplifies many problems in measure theory and helps establish connections between measurable functions and integration, as well as the area and coarea formulas.
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