In Wikipedia, https://en.wikipedia.org/wiki/Fubini%27s_theorem, it has been stated that:
The advantage of the Fubini–Tonelli over Fubini's theorem is that the repeated integrals of $|f|$ may be easier to study than the double integral. As in Fubini's theorem, the single integrals may fail to be defined on a measure $0$ set.
Would it be possible to ask for a clarifying example when this advantage plays a role? Unfortunately, there is no reference for this statement, which sounds interesting for me.