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Subjects
26-XX Real functions
26Bxx Functions of several variables
26B20 Integral formulas (Stokes, Gauss, Green, etc.)

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The area formula for $W^{1, n}$ -mappings

Jan Malý (1994)

Commentationes Mathematicae Universitatis Carolinae

Let $f$ be a mapping in the Sobolev space $W^{1, n} (Ω, 𝐑^{n})$ . 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.

The divergence theorem and Perron integration with exceptional sets

Wolfgang B. Jurkat (1993)

Czechoslovak Mathematical Journal

The fundamental theorem for the $ν_{1}$ -integral on more general sets and a corresponding divergence theorem with singularities

Wolfgang B. Jurkat, D. J. F. Nonnenmacher (1995)