## 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.

Author: Peter Mörters urn:nbn:de:hbz:386-kluedo-7879 Preprints (rote Reihe) des Fachbereich Mathematik (292) Preprint English 1995 1995 Technische Universität Kaiserslautern Palm distributions; average densities ; geometry of measures ; order-two densities ; tangent measure distributions Adv. Appl. Math. Fachbereich Mathematik 510 Mathematik 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 28A80 Fractals [See also 37Fxx] 60G57 Random measures

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