In order to compute the packing dimension of orthogonal projections Falconer and Howroyd  have introduced a family of packing dimension profiles Dims that are parametrized by real numbers s > 0. Subsequently, Howroyd  introduced alternate s-dimensional packing dimension profiles P-Dims by using Caratheodory-type packing measures, and proved, among many other things, that P-Dims E = Dims E for all integers s > 0 and all analytic sets E RN.
The aim of this paper is to prove that P-Dims E = Dims E for all real numbers s > 0 and analytic sets E RN. This answers a question of Howroyd [5, p. 159]. Our proof hinges on establishing a new property of fractional Brownian motion.
(Received November 13 2006)
(Revised October 23 2007)
† Research partially supported by NSF grant DMS-0404729.