Riemann-Lebesgue theorem for integrable functions

[fourier jr]

If f is integrable on $$(-\infty, \infty) = E$$ then $$\lim_{n\rightarrow\infty} \int_E f(x)cos(nx) = 0$$

it's supposed to be easy if f is a step function & then i can use another problem that was part of the homework, but i can't seem to figure out how that would work...





(ps- maybe i shouldn't call myself Fourier jr if I'm stuck on a problem like this )

 

[shmoe]

If f is a step function, break it up into the corresponding intervals. Can you show the integral restricted to anyone of these intervals goes to zero as n goes to infinity?

 

[fourier jr]

thx for the tip... i must have been thinking too hard about it...