Abstract
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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