Where can I find a straight-forward proof of Fubini's theorem for the Lebesgue integral on $\mathbb R^n$?
2026-03-26 15:40:28.1774539628
Reference Request - Fubini's Theorem
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Stein-Shakarchi's Princeton Lecture Series in Analysis III has a good proof.
Some probability books do a quicker job via the use of more auxiliary results. Jacob Rosenthal's First look at Rigorous Probability would be my rec.
Wheeden and Zygmund's Measure and Integral is a classic text.
I'd comment that proofs of Fubini's Theorem tend to be lengthy in nature. As far as "straight-forward" is concerned, I'd say the lengthier proofs also tend to be more direct which may be what you want when you say "straight-forward"?