Suppose $f$ and $g$ are real functions such that $f*g\in L^1$ Is there an example where Fubini's theorem might fail for the integral of the convolution? That is:
$$\int_X(\int_Yf(x-y)g(y)dy)dx\not=\int_Y(\int_Xf(x-y)g(y)dx)dy$$
I know that if $f,g\in L^1$ then by Tonelli the product $f(x-y)g(y)$ is integrable in $X\times Y$ and hence Fubini's theorem holds, but is there an example where that's not the case?