Comparative growth of composition of entire functions (Q1209009)

If \(f\) is a meromorphic function of finite order \(\lambda(0<\lambda<+\infty)\) in the plane, then \(f\) has at most two Borel exceptional values -- i.e. a-points for which \[ \lim\sup_{r\to\infty}\left(\left(\log n\left(r,{1\over f- a}\right)\right)/(\log r)\right)\neq\lambda. \] A set \(E\) in the plane is termed Borel removable if the conclusion of the theorem above holds when a-points are tallied only in \(\mathbb{C}\backslash E\). The author shows that for an entire function \(E\) may be the union of a sequence of discs whose radii tend to infinity. Removable sets for select differential polynomials in an entire function and for meromorphic functions are also discussed.