Hausdorff measure and packing measure of the graph of dilation-stable Lévy processes

Let be a dilation-stable Lévy process on Rd. We determine a Hausdorff measure function ϕ(a) such that the graph G[0,1]={(t,X(t)):0⩽t⩽1} has positive finite ϕ-measure. We also investigate the packing measure of G[0,1].