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Lebesgue's criterion

  1. Jan 10, 2007 #1


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    There's a theorem in my real analysis textbook that says

    A function f is Riemann-integrable iff the set of its points of discontinuity is of measure zero.

    But take say f(x)=1/x. It is only discontinuous as x=0, but it's not integrable on (-e,e). :grumpy:
  2. jcsd
  3. Jan 10, 2007 #2
    i could be wrong but i think that theorem only applies to bounded functions.
  4. Jan 10, 2007 #3
    This looks like a blatant omission of the word "bounded".
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