Average densities and linear rectifiability of measures

  • We show that a measure in a Euclidean space is linearly rectifiable if and only if the lower 1-density is positive and finite and agrees with the lower average 1-density almost everywhere.

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Metadaten
Author:Peter Mörters
URN:urn:nbn:de:hbz:386-kluedo-7893
Series (Serial Number):Preprints (rote Reihe) des Fachbereich Mathematik (294)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of first Publication:1999
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Rectifiability; average density; order-two density
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011