Hausdorff measure of critical set for Luzin $N$ condition
Functional Analysis
2025-10-14 v1
Abstract
It is well-known that there is a Sobolev homeomorphism for any which maps a set of zero Lebesgue -dimensional measure onto the set of positive measure. We study the size of this critical set and characterize its lower and upper bounds from the perspective of Hausdorff measures defined by a general gauge function.
Keywords
Cite
@article{arxiv.2005.06559,
title = {Hausdorff measure of critical set for Luzin $N$ condition},
author = {Anna Doležalová and Marika Hrubešová and Tomáš Roskovec},
journal= {arXiv preprint arXiv:2005.06559},
year = {2025}
}