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Math Help - riemann integrable problem

  1. #1
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    riemann integrable problem

    f is a function on [a,b] such that |f| is integrable . is it true that f must be integrable? give proof or counterexample
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  2. #2
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    another problem

    Attached Thumbnails Attached Thumbnails riemann integrable problem-untitled2.jpg  
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  3. #3
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    For the first question consider f(x) = \left\{ \begin{array}{c}1\mbox{ if }x\in \mathbb{Q} \\ -1\mbox{ if }x\not \in \mathbb{Q} \end{array} \right..

    For second question use \max (a,b) = \frac{1}{2}(a+b) - \frac{1}{2}|a-b|.
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