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the graph of continuous function $f:\Bbb{R}\to \Bbb{R}$ has measure $0$.

the graph of measurable function $f:\Bbb{R}\to \Bbb{R}$ is measurable. it can also be shown it has measure 0: The graph of a measurable function

But could you show me an example of:

  1. (noncontinuous) function with graph of positive measure?

  2. (nonmeasurable) function which has nonmeasurable graph?

Thanks in advance.

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victor1990
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    I think the graph of nontrivial solution of Cauchy equation has nonmeasurable graph. – Hanul Jeon Oct 06 '13 at 11:49
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    I found this: http://math.stackexchange.com/questions/35606/lebesgue-measure-of-the-graph-of-a-function But the answer is difficult for me. – Catcat Mar 27 '15 at 00:44
  • Any answer to this question will be like that; there are no nice examples one can "see". –  Oct 14 '15 at 04:09

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