Abstract: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 H\"older continuous. This exceptional set has Hausdorff dimension zero.
Keywords: Sobolev spaces, change of variables, area formula, H\"older continuity
AMS Subject Classification: 28A75, 26B15