Hausdorff measures, dyadic approximations, and the Dobiński set

摘要

The Dobiński set D is an exceptional set for a certain infinite product identity, whose points are characterized as having exceedingly good approximations by dyadic rationals. We study the Hausdorff dimension and logarithmic measure of D by means of the mass transference principle and by the construction of certain appropriate Cantor-like sets, termed willow sets, contained in D.