I am drawing a blank here. I know it has to do with the fact that the rationals are dense in the reals, but somehow it is not coming together for me. Any idea?
Let be defined by
Show that the iterated integral exists but that is not integrable.
I am supposed to use the following to prove the part where it is not integrable:
Suppose is bounded form the sum .
If the sequence converges to a limit as and if the limit is the same for any choice of sample points in , then we say that is integrable over .
In other words, I can't use the uppersum not equal to the lower sum strategy since it is not cover in class which I am taking now.
Any help is appreciated. Thanks for your time!