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Let $\mu$ denote a Borel probability measure and let $\{ \mu_{t} \}_{t\geq1}$ denote the free additive convolution semigroup of Nica and Speicher. Weshow that the support of these measures varies continuously in the Hausdorffmetric for $t >1$. We utilize complex analytic methods and, in particular, acharacterization of the absolutely continuous portion of these supports due toHuang.

On the Hausdorff Continuity of Free L\`evy Processes and Free Convolution Semigroups