Geodesic
The area formula for $W^{1,n}$-mappings
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 2, pp. 291-298.

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Let $f$ be a mapping in the Sobolev space $W^{1,n}(\Omega,\bold R^n)$. Then the change of variables, or area formula holds for $f$ provided removing from counting into the multiplicity function the set where $f$ is not approximately Hölder continuous. This exceptional set has Hausdorff dimension zero.
Classification : 26B15, 26B20, 28A75, 30C65, 46E35
Keywords: Sobolev spaces; change of variables; area formula; Hölder continuity 
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Malý, Jan. The area formula for $W^{1,n}$-mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 2, pp. 291-298. http://geodesic.mathdoc.fr/item/CMUC_1994__35_2_a9/