On Cantor sets and doubling measures
  For a large class of Cantor sets on the real-line, we find sufficient and necessary conditions implying that a set has positive (resp. null) measure for all doubling measures of the real-line. We also discuss same type of questions for atomic doubling measures defined on certain midpoint Cantor sets. 
Marianna Cs\"ornyei and Ville Suomala
math.CA