Practice question · True or false
Fubini's theorem lets you swap the order of integration for any bounded function.
Hints
- What does the theorem require of the integrand?
- Continuity, or absolute integrability.
Show the answer
False
Why
False. It needs continuity on the region, or, in the Lebesgue form, absolute integrability. Without it the two iterated integrals can genuinely differ, which is the point of the classic counterexamples. In practice the hypothesis almost always holds, but it is a hypothesis rather than a licence.
Practise Multiple Integration
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More questions on Multiple Integration
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