On the decomposition of an entire function of finite order into factors having given growth

In this paper the following result is proved:
Theorem. Let $\lambda_i,$ $i=1,\dots,n,$ be given such that $\lambda_i\geqslant0$ and $\sum\lambda_i=1$. Then any entire function $f(z)$ of finite order $\rho$ can be presented as a product of factors $f_i(z)$ such that
$$ \ln|f_i(z)|=\lambda_i\ln|f(z)|+o(|z|^\rho),\quad i=1,\dots,n, $$
as $z\to\infty,$ $z$ outside a $C_0$-set.
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