I am going through exercise problems of Rudin, and I came across this question.
Find an example of a positive continuous function $f$ in the open unit square in $\mathbb{R}^2$, whose integral (relative to Lebesgue measure) is finite but such that $\int_0^1 f_x(y) dy$ is infinite for some $x \in (0,1)$. (Here, $f_x(y) = f(x,y)$.)
I tried thinking of cases when Fubini theorem fails, for example $\displaystyle f(x,y) = \frac{2x-1}{y}$, but I found it difficult to evaluate the integral in Lebesgue sense.
Any help is greatly appreciated.