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I need to show that the following real valued function on $\mathbb{R}$ is nonmeasurable: $$ f(x) = \begin{cases} x &\text{$x \in E$} \\ -x &\text{$x \in [0,1] \setminus E$} \end{cases} $$

where $E$ is a non-measurable subset of $[0,1]$. How could one do this?

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