Lemma (Borel). If \(g_1,\cdots,g_n\) are entire functions such that
\[e^{g_1}+\cdots+e^{g_n}=1 \]then some \(g_i\) is constant.
(Equivalently, there do no exist \(n\) nonconstant entire functions, each omitting the value zero, such that their sum is \(1\).)
Proof. TODO
标签：entire,functions,Lemma,cdots,Borel,such From： https://www.cnblogs.com/chaliceseven/p/16849786.html