On an estimate for the size of an exceptional set in the lemma on the logarithmic derivative (Q1585637)

Let \(f\) be meromorphic in \(\mathbb{C}\). The lemma on the logarithmic derivative says that, for some exceptional set \(E(f)\), \[ m_{f'/f}(r)= O(\ln T_f(r)+ \ln r)\qquad (r\to\infty,\;r\not\in E(f)), \] where \(T_f\) is the Nevanlinna characteristic of \(f\) and \(m_{f'/f}\) is the proximity function of \(f'/f\). While for functions of finite order, \(E(f)\) is always empty, exceptional sets may occur in the infinite order case. In this paper, the author gives an exact estimate of the size of possible exceptional sets in the above lemma.