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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

[itex]\int f(t)dt=A=const.[/itex]

And now look at the function

[itex]G(\tau) = \int f(t - \tau)dt.[/itex]

Now, for any finite [itex]\tau[/itex], [itex]G(\tau)=A[/itex], obviously.

However, I asked myself what is the answer for [itex]\lim_{\tau \to +\infty}G(\tau)[/itex]?

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

[itex]\lim_{\tau \to +\infty}\int f(t - \tau)dt =\int \lim_{\tau \to +\infty}f(t - \tau)dt[/itex]

mainly because I haveno ideahow to interpret this

[itex]\lim_{\tau \to +\infty}f(t - \tau)[/itex]

So, what say you? I'm clueless.

Thanks!

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# A question about the limit of a specific function, but not sure how to formulate it

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