Measurable envelopes, Hausdorff measures and Sierpiński sets

Volume 98 / 2003

Márton Elekes Colloquium Mathematicum 98 (2003), 155-162 MSC: Primary 28E15; Secondary 28A78, 03E35. DOI: 10.4064/cm98-2-2


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.


  • Márton ElekesRényi Institute of Mathematics
    Reáltanoda u. 13–15
    Budapest 1053, Hungary

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