Prove that the conclusion of Fubini's theorem remain in force if we replace the condition that $f$ is integrable by $\int\left(\int\left|f_x(y)\right| d \mu_2(y)\right) d \mu_1(y)<\infty$.
My solution: Simply by Tonelli's theorem, we get $\int |f| d\mu=\int\left(\int\left|f_x(y)\right| d \mu_2(y)\right) d \mu_1(y)<\infty$. Now we have the usual hypothesis for Fubini's theorem.
I doubt the solution is correct since the qustion is worth more marks in the exam.
Any help is appreciated.