# Article

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Keywords:
Sobolev spaces; change of variables; area formula; Hölder continuity
Summary:
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.
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