A Dimension Theorem for Sample Functions of Processes with Stable Components

For processes $X(t)$ with stable components we calculate $\dim X(E)$ in terms of $\dim E$, where $E$ is a fixed Borel subset of [0, 1] of known Hausdorff-Besicovitch dimension, $\dim E$. Our results extend the earlier ones of Blumenthal and Getoor in the stable case.