# Homework Help: Help with Riemann-Lebesgue theorem pls

1. Oct 21, 2004

### 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 :uhh: )

2. Oct 21, 2004

### shmoe

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

3. Oct 22, 2004

### fourier jr

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

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook