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Prove that if $A$ is null and $f: \mathbb{R} \longrightarrow \mathbb{R}$ has a continuous derivative, then $f(A)$ is null.

I think it has something to do with the fact that $f'$ is bounded in any interval, but I'm at a complete loss as to how to take it further. Any help much appreciated.

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    Do you know about absolutely continuous functions? They preserve null sets, and any function with a continuous derivative is absolutely continuous.2012-04-26

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