Measurable Envelopes, Hausdorff Measures and Sierpi\'nski Sets
  We show that the existence of measurable envelopes of all subsets of $\RR^n$ with respect to the $d$-dimensional Hausdorff measure $(0<d<n)$ is independent of $ZFC$. We also investigate the consistency of the existence of Sierpi\'nski sets measurable with respect to the $d$-dimensional Hausdorff measure. 
M\'arton Elekes
math.CA math.LO