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Average densities and linear rectifiability of measures

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

P. Mörters
P. Mörters
Affiliation:
Universität Kaiserslautern, Fachbereich Mathematik, 67663 Kaiserslautern, Germany.
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Abstract

We show that a measure on ℝd is linearly rectifiable if, and only if, the lower l-density is positive and finite and agrees with the lower average l-density almost everywhere.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 44 , Issue 2 , December 1997 , pp. 313 - 324
Copyright
Copyright © University College London 1997

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