arXiv:1309.3094 Abstract | arXiv Analytics

arXiv:1309.3094 [math.CA]Abstract References Reviews Resources

Luzin's Condition (N) and Modulus of Continuity

Published 2013-09-12Version 1

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.

Categories: math.CA

Subjects: 26B15, 26B35, 46E35

Keywords: continuity, sobolev-orlicz spaces, mapping violates luzins condition, exceptional set, cantor set

Related articles: Most relevant | Search more

arXiv:2411.04959 [math.CA] (Published 2024-11-07)

Bounding the dimension of exceptional sets for orthogonal projections

Peter Cholak, Marianna Csornyei, Neil Lutz, Patrick Lutz, Elvira Mayordomo, D. M. Stull

arXiv:2211.02190 [math.CA] (Published 2022-11-03)

On the packing dimension of exceptional sets of projections

Ryan E. G. Bushling

arXiv:1611.07692 [math.CA] (Published 2016-11-23)

On exceptional sets of Hilbert transform