By Fubini-Tonelli theorem, if one of $\int(\int |f(x,y)| dy)dx$, $\int(\int |f(x,y)| dx)dy$, $\int\int |f(x,y)| dxdy$ is finite , then $\int(\int f(x,y) dy)dx = \int(\int f(x,y) dx)dy=\int \int f(x,y) dxdy$. Does this imply that the following cases are impossible,
(i)Both of the iterated integrals exist and agree but the double integral does not exist.
(ii)At least one of the iterated integrals is finite but they are not equal.