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Thread: Monotone Convergence

  1. #1
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    Monotone Convergence



    Monotone Convergence Theorem:


    I know this almost follows from the theorem. But I first need to write \displaystyle \int_{I_n} f = \int_S f_n for some f_n in such a way that (f_n) is an increasing sequence tending to f. (Then we have something that satisfies the hypotheses of the theorem.) What f_n could I use?
    Then in the case of any function g can I consider positive and negative parts?
    Last edited by ProofbyInduction; Apr 18th 2012 at 03:10 PM.
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  2. #2
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    Re: Monotone Convergence

    Define f_n(x)= f(x) if x\in I_n, f_n(x)= 0 otherwise.
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