Luzin's Condition (N) and Modulus of Continuity
Classical Analysis and ODEs
2013-09-13 v1
Abstract
In this paper, we establish Luzin's condition (N) for mappings in certain Sobolev-Orlicz spaces with certain moduli of continuity. Further, given a mapping in these Sobolev-Orlicz spaces, we give bounds on the size of the exceptional set where Luzin's condition (N) may fail. If a mapping violates Luzin's condition (N), we show that there is a Cantor set of measure zero that is mapped to a set of positive measure.
Cite
@article{arxiv.1309.3094,
title = {Luzin's Condition (N) and Modulus of Continuity},
author = {Pekka Koskela and Jan Malý and Thomas Zürcher},
journal= {arXiv preprint arXiv:1309.3094},
year = {2013}
}