A Uniqueness Result Related to Meromorphic Functions Sharing Two Sets

With the help of a new unique range set we investigate the well known question of Gross and prove a uniqueness theorem on meromorphic functions sharing two sets. The result in this paper will improve and supplement some earlier results. In this paper, by meromorphic functions we will always mean meromorphic functions in the complex plane. We adopt the standard notations of the Nevanlinna theory of meromorphic functions as explained in. It will be convenient to let E denote any set of positive real numbers of finite linear measure, not necessarily the same at each occurrence.