On the Hausdorff measure of the Julia set and the escaping set of entire functions with regularly growing maximum modulus

Abstract

Abstract. We prove that the Hausdorff measure of the escaping set and the Julia set of an entire function f is infinite with respect to certain gauge functions, provided that f is outside of the Eremenko-Lyubich class, and that the maximum modulus M (r, f ) of f satisfies a certain regularity condition.