ON THE SIZE OF THE SET WHERE A MEROMORPHIC FUNCTION IS LARGE

Abstract

In this paper, we investigate the extent of the set on
which the modulus of a meromorphic function is lower bounded by a
term related to some Nevanlinna Theory functionals. A. I. Shcherba
estimate the size of the set on which the modulus of an entire func-
tion is lower bounded by 1. Our theorem in this paper shows that
the same result holds in the case that the lower bound is replaced
by lT (r, f ), 0 ≤ l < 1 , which improves Shcherba’s result. We also
give a similar estimation for meromorphic functions.