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Lebesgue Integrable Function question

  1. Apr 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Let f be a Lebesgue integrable function in the interval [a,b]

    Show that:

    lim integral from a to b (f(x)*|cosnx|) = 2/pi * integral from a to b (f(x))
    n->infinity

    2. Relevant equations

    Every measurable function can be approximated arbitrarily close by simple functions.

    3. The attempt at a solution

    I've solved part i of the problem (which was to show the same setup except f*cosnx instead of f*|cosnx|) has an integral equal to zero.

    I'm pretty stuck on this part - I'm sure I have to find a simple function but I'm not sure what a good simple function would be.
     
  2. jcsd
  3. Apr 30, 2009 #2
    Can you prove this is true for the special case when f is the characteristic function of an interval I=[r,s], where [r,s] is a subset of [a,b]?
     
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