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Does there exist a function $f:\mathbb R \rightarrow \mathbb R$ such that the set $E=\{(x,f(x)\mid x\in\mathbb R\}$ is non-measurable in $\mathbb R^2$?

Michael Hardy
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happymath
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  • See:

    http://math.stackexchange.com/questions/35606/lebesgue-measure-of-the-graph-of-a-function

     – ploosu2 Apr 28 '14 at 18:01
  • @ploosu2 i am asking for a non measurable set and in the other question he is asking for positive measure. I can clearly see positive measure is not possible that is why i am asking for non measurable set – happymath Apr 28 '14 at 18:08
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    In the answer a graph with positive outer measure (and hence non-measurable) is constructed. – ploosu2 Apr 28 '14 at 18:10
  • @ploosu2 ok i get it thanks but i am not very comfortable with transfinite induction and the other set theoretic ideas is there something simpler? – happymath Apr 28 '14 at 18:11

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