Measurable envelopes, Hausdorff measures and Sierpiński sets
Volume 98 / 2003
Colloquium Mathematicum 98 (2003), 155-162
MSC: Primary 28E15; Secondary 28A78, 03E35.
DOI: 10.4064/cm98-2-2
Abstract
We show that the existence of measurable envelopes of all subsets of ${\Bbb R}^n$ with respect to the $d$-dimensional Hausdorff measure $(0< d< n)$ is independent of ZFC. We also investigate the consistency of the existence of ${\cal H}^d$-measurable Sierpiński sets.
