Hausdorff measure of the scattered Cantor sets (Q2782772)

The authors consider an invariant of the classical Cantor set: the relative position of basic intervals may change arbitrarily at each generation, but keep the same scaling 1/3 and open set condition. It is easy to see that the Hausdorff dimension of this class of sets is \(\frac{\log 2}{\log 3}\). Then the authors estimate the Hausdorff measure in dimension \(\frac{\log 2}{\log 3}\) of this class, which in general differs from 1 (the Hausdorff measure of the classical Cantor set).