The error term in Nevanlinna's inequality

An upper bound is given for the error term S(r, {aj}, f) in Nevanlinna's inequality. For given positive increasing functions p and φ with . We prove thatholds, with a small exceptional set of r, for any finite set of points {aj} in the extended plane and any meromorphic function f such that Ψ(T(r, f))=O(P(r)). This improves the known results of A. Hinkkanen and Y. F. Wang. The sharpness of the estimate is also considered.