  In this article we study for which Cantor sets there exists a gauge-function
h, such that the h-Hausdorff-measure is positive and finite. We show that the
collection of sets for which this is true is dense in the set of all compact
subsets of a Polish space X. More general, any generic Cantor set satisfies
that there exists a translation-invariant measure mu for which the set has
positive and finite mu-measure.
  In contrast, we generalize an example of Davies of dimensionless Cantor sets
(i.e. a Cantor set for which any translation invariant measure is either zero
or non-sigma-finite, that enables us to show that the collection of these sets
is also dense in the set of all compact subsets of a Polish space X.
