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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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

Author: Bernd Kirchheim
Journal: Proc. Amer. Math. Soc. 121 (1994), 113-123
MSC: Primary 28A78
MathSciNet review: 1189747
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Abstract: 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.

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Keywords: Rectifiability, metric differential, Hausdorff measure, density, Kolmogoroff measure
Article copyright: © Copyright 1994 American Mathematical Society

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