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Unbounded and continuous almost everywhere

  1. Feb 27, 2009 #1
    Can anyone give me an example of a function f:[a,b]->R which is continuous almost everywhere yet unbounded?

    Thanks!
     
  2. jcsd
  3. Feb 27, 2009 #2
    The function f:[0,1]->R given by
    f(x) = n if x=1/n for some positive integer n
    f(x) = 0 else
     
  4. Feb 27, 2009 #3
    muchas gracias
     
  5. Feb 27, 2009 #4
    Okay how about one which isn't Riemann (improper) integrable
     
  6. Mar 15, 2009 #5
    [tex]\displaystyle\sum_{ k = 1 }^\infty k \chi_{ [ 0, \frac{ 1 }{ k^2 } ] }[/tex]
     
  7. Mar 15, 2009 #6

    matt grime

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    Um, surely f(x)=1/x for x>0 and f(0)=0 is far simpler, and does everything needed.
     
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