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Example of a SEQUENCE of integrable functions that converges point wise to a non-inte

  1. Feb 9, 2009 #1
    hey guys,
    Any one can think of any examples ?
    Of a sequence of integrable functions{fn} on [0,1] that converges pointwise to a non-integrable function f:[0,1] --> R
    ??
     
  2. jcsd
  3. Feb 10, 2009 #2

    mathman

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    Re: Example of a SEQUENCE of integrable functions that converges point wise to a non-

    fn=1/x for x>1/n, fn=n for x<1/n.
     
  4. Feb 11, 2009 #3
    Re: Example of a SEQUENCE of integrable functions that converges point wise to a non-

    mathman, I don't believe that function converges pointwise (specifically at 0). Setting fn(0) = 0 will fix that, though.
     
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