Tangent measure distributions of fractal measures

  • Tangent measure distributions are a natural tool to describe the local geometry of arbitrary measures of any dimension. We show that for every measure on a Euclidean space and every s, at almost every point, all s-dimensional tangent measure distributions define statistically self-similar random measures. Consequently, the local geometry of general measures is not different from the local geometry of self-similar sets. We illustrate the strength of this result by showing how it can be used to improve recently proved relations between ordinary and average densities.

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Author:Peter Mörters, David Preiss
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7902
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (295)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Tag:Palm distributions ; average densities ; geometric measure theory ; order-two densities; tangent measure distributions
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
28A80 Fractals [See also 37Fxx]
60G57 Random measures

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