One of the main tools in geometric function theory is the fact that the area formula is true for Lipschitz mapping; if f is differentiable a.e. (in the classic sense) then f can be exhausted up to a set of zero measure; the restriction of f, set by set, is Lipschitz [6, Theorem 3.18]. The aim of this survey is to clarify the regularity assumptions for a map to be differentiable a.e., and to give some auxiliary results when it is not, using the notion of approximate differentiability.
Published September 15, 2018.
Math Subject Classifications: 46E35.
Key Words: Sobolev homeomorphism; Lusin condition; approximate differentiability.
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| Luigi D'Onofrio |
University of Napoli "Parthenope", Italy
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