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Math Help - Prove that this function is integrable

  1. #1
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    Exclamation Prove that this function is integrable

    Hey, guys! I'm a poor student from Nigeria. And i need your help!



    I need to prove that this function is integrable (or not integrable)
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  2. #2
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    Do you mean Riemann or Lebesgue integrable?
    If Lebesgue then the integral would be 0 since it is only nonzero on a set with measure 0.
    As for Riemann, i don't think it's integrable since you should be able to make the difference between the upper and lower sums arbitrarily large (use the fact that \mathbb{Q} is a dense subset of \mathbb{R})
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  3. #3
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    Quote Originally Posted by putnam120 View Post
    Do you mean Riemann or Lebesgue integrable?
    If Lebesgue then the integral would be 0 since it is only nonzero on a set with measure 0.
    I mean Lebesgue integrable, thank you for your answer!
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