Definition 5.15.4EC0662753F9C

Definition 5.15.4.EC0662753F9C A subset $E\subseteq \Omega $ is thin¹ at $x\in \Omega $ if one of the following conditions holds:

1. 2F25DFCC541C

   $x\not\in \overline{E}$;

2. 9A680A93372A

   $x\in \overline{E}$ and there is an open neighborhood $U\subseteq \Omega $ of $x$ and $\varphi \in \mathrm{PSH}(U)$ such that

   \[ \varlimsup _{(U\cap E)\setminus \{ x\} \ni y\to x} \varphi (y)<\varphi (x). \]

We say $E$ is thin if it is thin at all $x\in \Omega $.