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Type of convergences

  1. Apr 22, 2014 #1
    1. The problem statement, all variables and given/known data

    Let fn be a sequence of measurable functions converges to f a.e. Is it possible to get a subsequence fnk of fn s.t. fn converges in L1 ?

    2. The attempt at a solution
    I have proved the converse statement is true and i guess the above statement is impossible but I fail to prove it.
     
  2. jcsd
  3. Apr 22, 2014 #2

    jbunniii

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    Hint: Look for a counterexample where ##f_n \rightarrow 0## pointwise but ##\|f_n\| = 1## for all ##n##.
     
  4. Apr 22, 2014 #3
    Thanks for your suggestion
     
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