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Math Help - Convergence in measure

  1. #1
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    Convergence in measure

    If f_{n} \to f in measure then prove that |f_n|->|f| in measure.
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    Quote Originally Posted by Chandru1 View Post
    If f_{n} \to f in measure then prove that |f_n|->|f| in measure.
    What does f_{n} \to f in measure mean? That the integrals converge?
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  3. #3
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    Quote Originally Posted by southprkfan1 View Post
    What does f_{n} \to f in measure mean? That the integrals converge?
    Nope it means \mu(|f_n-f|>\epsilon) \rightarrow 0.

    Quote Originally Posted by Chandru1 View Post
    If f_{n} \to f in measure then prove that |f_n|->|f| in measure.
    Have you heard of the reverse triangle inequality?  ||x|-|y|| \leq |x-y|. Use it to prove that \{||f_n|-|f||> \epsilon\} \subset \{|f_n-f|> \epsilon\}.
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