Sets non-thin at \infty in \Bbb C ^m, and the growth of sequences of entire functions of genus zero

In this paper we define the notion of non-thin at $\mathrm{\infty }$ as follows: Let $E$ be a subset of ${\mathbb{C}}^m$. For any $R>0$ define $E_R=E\cap {z\in \Bbb C ^m :|z|\leq R}$\mathrm{.}Wesaythat$E$isnon-thinat$\infty$ if \lim_{R\to\infty}V_{E_R}(z)=0 for all $z\in {\mathbb{C}}^m$, where $V_E$ is the pluricomplex Green function of $E$. This definition of non-thin at $\mathrm{\infty }$ has good properties: If $E\subset \Bbb C^m$isnon-thinat$\infty$and$A$ispluripolarthen$E\backslash A$ is non-thin at $\mathrm{\infty }$, if $E\subset {\mathbb{C}}^m$ and $F\subset {\mathbb{C}}^n$ are closed sets non-thin at $\mathrm{\infty }$ then $E\times F\subset {\mathbb{C}}^m\times {\mathbb{C}}^n$ is non-thin at $\mathrm{\infty }$ (see Lemma \ref{Lem1}). Then we explore the properties of non-thin at $\mathrm{\infty }$ sets and apply this to extend the results in \cite{mul-yav} and \cite{trong-tuyen}.