Measurable Envelopes, Hausdorff Measures and Sierpi\'nski Sets
classification
🧮 math.CA
math.LO
keywords
hausdorffmeasurabledimensionalenvelopesexistencemeasurenskirespect
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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.
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