Symmetry properties of average densities and tangent measure distributions of measures on the line

  • Answering a question by Bedford and Fisher we show that for every Radon measure on the line with positive and finite lower and upper densities the one-sided average densities always agree with one half of the circular average densities at almost every point. We infer this result from a more general formula, which involves the notion of a tangent measure distribution introduced by Bandt and Graf. This formula shows that the tangent measure distributions are Palm distributions and define self-similar random measures in the sense of U. Zähle.

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Metadaten
Author:Peter Mörters
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7879
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (292)
Document Type:Preprint
Language of publication:English
Year of Completion:1995
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Tag:Palm distributions; average densities ; geometry of measures ; order-two densities ; tangent measure distributions
Source:Adv. Appl. Math.
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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