Rectifiable metric spaces: local structure and regularity of the Hausdorff measure

  title={Rectifiable metric spaces: local structure and regularity of the Hausdorff measure},
  author={Bernd Kirchheim},
We consider the question whether the "nice" density behaviour of Hausdorff measure on rectifiable subsets of Euclidian spaces preserves also in the general metric case. For this purpose we show the existence of a metric differential of Lipschitzian functions also in situations where the well-known theorem of Rademacher fails. Let (X, p) be a metric space. We denote by g%n the n-dimensional Hausdorff measure over X defined by Zn(E) _ p (E) =li in f { () (diamp(Ei))n I E c U Ei, diamp(Ei) 1… 
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Czechoslovakia Current address : Institut für Mathematik, Johannes Kepler Universität, Altenbergerstrasse, A4040 Linz, Austria E-mail address : kir chhe iQmf f. uniba
  • Institute of Applied Mathematics, Comenius University Bratislava, Mlynská dolina, Bratislava
  • 1992