Dimensional coincidence does not imply measure-theoretic tameness
Volume 242 / 2018
Fundamenta Mathematicae 242 (2018), 103-107
MSC: Primary 03C64; Secondary 28A78.
DOI: 10.4064/fm427-8-2017
Published online: 12 February 2018
Abstract
We show that there is a compact $C^0$ submanifold $M$ such that the Hausdorff measure of $M$ is $\infty$ and if $\mathfrak R$ is an o-minimal expansion of the real field that is exponentially bounded, then $(\mathfrak R,M)$ does not define $\mathbb Z$.
