= Solution
For product measure spaces, <Tonelli's theorem> states that for a nonnegative <measurable function> the product-space integral equals either iterated integral, allowing the value $+\infty$. Fubini's theorem states that if a <measurable function> has finite integral of its absolute value, then its sections are <integrable> <almost everywhere>, both iterated integrals exist and equal the product-space integral. The absolute-integrability hypothesis is what permits this conclusion for a signed function. These statements apply to the Lebesgue product spaces used here, which are sigma-finite.
Back to article page
