Rational approximation and pluripolar sets

The main result in the article is
Theorem. Let $S\subset\mathbf C^n$ be a closed set such that $0\notin S$ and $\mathbf C^n\setminus S$ is a pseudoconvex domain. If for almost every complex line $l$ passing through $0$ the intersection $l\cap S$ is polar in $l$, then $S$ is a pluripolar set in $\mathbf C^n$.
This theorem is then applied to the analysis of sets of singularities of holomorphic functions which are rapidly approximated by rational functions.
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