I was thinking of this problem for a couple of hours, but wasn't sure how to formulate it, hence I wasn't able to google it.
It's pretty simple to explain, though. Observe any function with a finite integral over the R line
And now look at the function
Now, for any finite , , obviously.
However, I asked myself what is the answer for ?
I'm not sure if I have or don't have the right to exchange the limit and the integral
mainly because I have no idea how to interpret this
So, what say you? I'm clueless.