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arXiv · 1309.3094

Luzin's Condition (N) and Modulus of Continuity

Pekka Koskela·Jan Malý·Thomas Zürcher
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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.

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Pekka Koskela, Jan Malý, Thomas Zürcher. 2013-09-12. Luzin's Condition (N) and Modulus of Continuity. https://arxiv.org/abs/1309.3094

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