Measurable Envelopes, Hausdorff Measures and Sierpi\'nski Sets
Abstract
We show that the existence of measurable envelopes of all subsets of 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.
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