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Possible Duplicate:
Riemann Integrable $f$ and Real Analysis Proofs

I am solving old comprehensive real analysis exams and there are two questions that I can not be sure,

  1. If $f$ is Riemann integrable then $|f|^r$ is riemann integrable for any $r>0$.( True or False) I feel it is wrong indeed but couldn't find any counter example)

  2. $1 < p < q < r < \infty$ a function which is in $L^q$ but not in $L^p$ and not in $L^r$.

Thank you for any help.

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    Please do not double post. Your question [here](http://math.stackexchange.com/questions/259769/riemann-integrable-f-and-real-analysis-proofs), which is identical, has received one upvote and will most likely be addressed or is in the process of being addressed.2012-12-16

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