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Thin sets in $${\mathbb{C}}^ n$$. (English) Zbl 0575.32018
A subset E of $${\mathbb{C}}^ n$$, $$n\geq 1$$, is said to be thin at $$z_ 0\in \bar E$$ if there is a plurisubharmonic function f such that $$\overline{\lim}_{z\to z_ 0,\;z\in E,\;z\neq z_ 0} f(z)<f(z_ 0).$$
In this paper thinness is studied in connection with polynomial convexity. Also, a Jordan arc in $${\mathbb{C}}^ 2$$ is constructed which is thin at one of it’s points.
In the reference list, there is a misprint: References [4] and [5] are due to the author.

##### MSC:
 32U05 Plurisubharmonic functions and generalizations 32E20 Polynomial convexity, rational convexity, meromorphic convexity in several complex variables 31C10 Pluriharmonic and plurisubharmonic functions