%0 Journal Article
%T Luzin's Condition (N) and Modulus of Continuity
%A Pekka Koskela
%A Jan Maly
%A Thomas Zščrcher
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1309.3094v1