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Let $f$ and $g$ be Riemann integrable (real) functions and

$$f(x)\leq h(x)\leq g(x).$$

Is it true that $h(x)$ is Riemann integrable? Can someone post a proof (if there is)?

Thanks.

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    There exists bounded functions which are not Riemman integrable. Therefore no, that is not true: pick any bounded function $h$ which is not integrable in $[0,1]$, and suppose that $|h(x)|\leq M$ for all $x$. Then set $f(x)=-M$ and $g(x)=M$.2011-11-26

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