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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Author:Peter Mörters
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7893
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (294)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Tag:Rectifiability ; average density ; order-two density
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]

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