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Math Help - Convergence comparison

  1. #1
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    Convergence comparison

    Suppose that f_n\to f in measure and |f_n|\le g\in L^1, for all n. Show that f_n\to f in L^1. That is \lim_n\int_X|f_n-f|d\mu=0.

    I have already shown that \int_Xfd\mu=\lim_n\int_X f_nd\mu, but don't see how to use this or anything else to get to the desired result.
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  2. #2
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    Look at Dominated convergence theorem - Wikipedia, the free encyclopedia, the given proof of the assertion that you already know contains your desired result.
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