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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.

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