# Article

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Keywords:
boundary behavior of power series; exceptional set
Summary:
For $z\in \partial B^n$, the boundary of the unit ball in $\mathbb{C}^n$, let $\Lambda (z)=\lbrace \lambda \:|\lambda |\le 1\rbrace$. If $f\in \mathbb{O}(B^n)$ then we call $E(f)=\lbrace z\in \partial B^n\:\int _{\Lambda (z)}|f(z)|^2\mathrm{d}\Lambda (z)=\infty \rbrace$ the exceptional set for $f$. In this note we give a tool for describing such sets. Moreover we prove that if $E$ is a $G_\delta$ and $F_\sigma$ subset of the projective $(n-1)$-dimensional space $\mathbb{P}^{n-1}=\mathbb{P}(\mathbb{C}^n)$ then there exists a holomorphic function $f$ in the unit ball $B^n$ so that $E(f)=E$.
References:
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