Measure Theory · Calculus
Product Measures and Fubini’s Theorem
Fubini’s theorem licenses switching the order of integration when the function is non-negative or absolutely integrable. When neither holds, the iterated integrals can differ.
WHAT STUDENTS WILL LEARN
✓Construct the product measure
✓State Fubini’s theorem for iterated integrals
✓Apply Tonelli’s theorem to non-negative functions
✓Recognize when Fubini fails
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