Originally Posted by

**lajka** Hi,

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

$\displaystyle \int f(t)dt=A=const.$

And now look at the function

$\displaystyle G(\tau) = \int f(t - \tau)dt.$

Now, for any finite $\displaystyle \tau$, $\displaystyle G(\tau)=A$, obviously.

However, I asked myself what is the answer for $\displaystyle \lim_{\tau \to +\infty}G(\tau)$?

I'm not sure if I have or don't have the right to exchange the limit and the integral

$\displaystyle \lim_{\tau \to +\infty}\int f(t - \tau)dt =\int \lim_{\tau \to +\infty}f(t - \tau)dt$

mainly because I have *no idea* how to interpret this

$\displaystyle \lim_{\tau \to +\infty}f(t - \tau)$

So, what say you? I'm clueless.

Thanks!