The packing measure of the support of super-Brownian motion

Our object is to obtain more information about the fractal properties of super-Brownian motion. For d ⩾ 2 the closed support S(Yt) of super-Brownian motion has zero Lebesgue measure and fractal dimension 2. The exact Hausdorff measure properties of S(Yt) are also known. In this paper we show that, for d ⩾ 3 there is no measure function ø such that the packing measure ø − p(S(Yt)) is finite and positive, and give an integral test which distinguishes those ø which make the packing measure 0 or +∞. Incomplete results are also obtained for d = 2.