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Help with Riemann-Lebesgue theorem pls

  1. Oct 21, 2004 #1
    If f is integrable on [tex](-\infty, \infty) = E[/tex] then [tex]\lim_{n\rightarrow\infty} \int_E f(x)cos(nx) = 0 [/tex]

    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. jcsd
  3. Oct 21, 2004 #2


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    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?
  4. Oct 22, 2004 #3
    thx for the tip... :smile: i must have been thinking too hard about it... :redface:
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