Derivative measures

Abstract

A characterization of those measures which are distribution derivatives is undertaken. For functions of n variables in BVC, the derivative measures are absolutely continuous with respect to Hausdorff n − 1 n - 1 measure. For functions in W 1 1 W_1^1 they are absolutely continuous with respect to n measure. For linearly continuous functions the derivative measures are zero for sets whose Hausdorff n − 1 n - 1 measure is finite. For n = 1 n = 1 , since n − 1 = 0 n - 1 = 0 , this reduces to the standard facts.