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Suppose $U$ is a bounded open set in $\mathbb{R}^m$ with ($m\geq2$). Is it possible to have a non-empty set $E$ in the boundary $ \partial U$ of $U$ that is open in $ \partial U$ and is polar? A set $E$ is called polar if there exists a superharmonic function on an open neighborhood of $E$ that takes the value of $\infty$ at each point of $E$.

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    $\begingroup$ What do you mean by a polar set? $\endgroup$ Jun 21, 2021 at 3:03
  • $\begingroup$ Sorry! I added the definition. $\endgroup$
    – M. Rahmat
    Jun 21, 2021 at 4:18

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