For beta-dynamical systems with integer bases, the Hausdorff f-measure of shrinking target sets is zero or full according to divergence of an explicit series.
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Dichotomy laws for the Hausdorff measure of shrinking target sets in $\beta$-dynamical systems
For beta-dynamical systems with integer bases, the Hausdorff f-measure of shrinking target sets is zero or full according to divergence of an explicit series.