= Solution
On a product of sigma-finite <measure spaces>, <Tonelli's theorem> says that a nonnegative measurable <function> has equal product and iterated integrals, allowing $+\infty$.
<Fubini's theorem> says that if a measurable <function> is absolutely integrable on the product, almost every section is integrable, the integrals of sections are integrable, and both iterated integrals equal the product integral. In particular, to establish absolute integrability one can first apply <Tonelli's theorem> to the absolute value and show its iterated integral is finite.
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