English

Measurable Envelopes, Hausdorff Measures and Sierpi\'nski Sets

Classical Analysis and ODEs 2011-09-27 v1 Logic

Abstract

We show that the existence of measurable envelopes of all subsets of \RRn\RR^n with respect to the dd-dimensional Hausdorff measure (0<d<n)(0<d<n) is independent of ZFCZFC. We also investigate the consistency of the existence of Sierpi\'nski sets measurable with respect to the dd-dimensional Hausdorff measure.

Keywords

Cite

@article{arxiv.1109.5305,
  title  = {Measurable Envelopes, Hausdorff Measures and Sierpi\'nski Sets},
  author = {Márton Elekes},
  journal= {arXiv preprint arXiv:1109.5305},
  year   = {2011}
}