Measurable Envelopes, Hausdorff Measures and Sierpiński Sets

Abstract

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 Sierpiński sets measurable with respect to the $d$-dimensional Hausdorff measure.

References in corpus (1)

• Measurability of functions with approximately continuous vertical sections and measurable horizontal sections