Note on the Nevannlinna proximity function

Abstract:

Let $\lambda$ be a positive function on $(0,\infty )$ with ${\lim _{r \to \infty }}\lambda (r) = \infty$, and A an arbitrary set of capacity zero. An example is given of a meromorphic function f for which $m(r,a) \to \infty ,r \to \infty$, whenever $a \in A$, and $T(r,f) = O[{(\log r)^2}\lambda (r)],r \to \infty$ .