For the purpose of change of variables in integral, it is important to know how to verify Luzin’s condition (N) for Sobolev mappings. In this article we survey some results on this topic sorted according to the method. We discuss the method of absolute continuity, results obtained via degree, and results based on the interplay between integrability and modulus of continuity.
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Pekka Koskela, Jan Malý, Thomas Zürcher, Luzin’s condition (N) and Sobolev mappings. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 23 (2012), no. 4, pp. 455–465DOI 10.4171/RLM/639