Fractal measures for meromorphic functions of finite order

Abstract

We prove several essential fractal properties, such as positivity, finiteness or local infinity, of Hausdorff and packing measures of radial Julia sets for large subclasses of entire and meromorphic functions considered in our previous work: çGeometric thermodynamical formalism and real analyticity for meromorphic functions of finite order'. Most of the results proven are shown to be optimal.