Separating covering numbers and separating uniformity numbers of Hausdorff measures need large continuum

Tatsuya Goto

We show that if $\mathfrak{c}={\aleph }_2$ then all covering numbers of Hausdorff measures $\mathrm{cov}({\mathcal{N}}^s({\mathbb{R}}^d))$ ($0<s<d,d\in \omega$) are equal and all…