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Convergence integral problem

  1. Oct 6, 2013 #1
    1. The problem statement, all variables and given/known data
    I have the attached file as an exercise for class. Problem is that I don't really understand why my book spends so much into solving it, when for me it seems pretty easy.

    2. Relevant equations
    Lebesgue dominated convergence theorem

    3. The attempt at a solution
    I thought that since the integrals of g and G are finite they are integrable. Also f_k is integrable for all k. Since f_k is squeezed between g_k and G_k we must have that either lfl≤lGl, which is integrable
    So lfl is no matter what bounded by an integrable function and we can use the Lebesgue dominated convergence theorem. Why is this not a correct approach?
    Is it because finite integral does not imply integrability? I don't see why it wouldn't.

    Attached Files:

  2. jcsd
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