Could you please help me with this:
show that for -T<t<T, the function defined by
is Lebesgue integrable and that
We are allowed to use results from Lebesgue integration.
Thanks in advance!
One way would be to use Fubini's theorem. Start with the fact that . The justification for that is that is dominated by and therefore integrable over ; and the integral is equal to
Integrate with respect to t to see that . Now use Fubini to change the order of integration and deduce that (after replacing T by t).
Now repeat the process: integrate from t=0 to T again, use Fubini, and conclude that . Finally, integrate by parts to see that .