Derivative Measures

Abstract

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 measure. For functions in Wx they are absolutely continuous with respect to n measure. For linearly continuous functions the derivative measures are zero for sets whose Hausdorff n -1 measure is finite. For n = 1, since « -1=0, Üús reduces to the standard facts.

Metric-measure boundary and geodesic flow on Alexandrov spaces

“…Hence we need to verify them only in a regular chart U, which we identify with its image φ(U) ⊂ R n . The first statement follows directly from the continuity of the metric tensor g on the subset U ∩ R and the result of [GL80] cited above.…”