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Abstract: Answering a question by Bedford and Fisher in [4] we show that for the circular and one-sided average densities of a Radon measure on the line with positive lower and nite upper -densities the following relations hold -almost everywhere We infer the result from a more general formula, which is proved by means of a detailed study of the structure of the measure and which involves the notion of tangent measure distributions introduced by Bandt ([2]) and Graf ([9]). We show that ... (Update)
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BibTeX entry: (Update)
@misc{ rters-symmetry,
author = "Peter Mörters",
title = "Symmetry Properties of Average Densities and Tangent Measure Distributions
of Measures on the Line",
url = "citeseer.ist.psu.edu/761328.html" }
Citations (may not include all citations):188 Geometric Measure Theory (context) - Federer - 1968
114 The Geometry of Sets and Measures in Euclidean Spaces (context) - Mattila - 1995
33 Akademie-Verlag (context) - Kallenberg, Measures - 1983
32 Analogues of the Lebesgue density theorem for fractal sets o.. (context) - Bedford, Fisher - 1992
29 On Bandt's tangential distribution for self-similar measures (context) - Graf - 1995
20 Random self-similar multifractals - Arbeiter, Patzschke - 1994
18 Wavelet transforms and order-two densities of fractals (context) - Falconer - 1992
16 The tangent distribution for self-similar measures (context) - Bandt - 1992
13 Order-two density of sets and measures with nonintegral dime.. (context) - Falconer, Springer - 1995
11 Tangent Measure Distributions and the Geometry of Measures (context) - orters - 1995
9 auf lokalkompakten abelschen Gruppen (context) - Mecke, are et al. - 1967
9 Self-similar random measures IV (context) - Patzschke, ahle - 1990
8 two density and the strong law of large numbers (context) - Marstrand - 1996
8 Self-similar random measures are locally scale invariant (context) - Patzschke, ahle - 1993
7 On linear sets of points of fractional dimension (context) - Besicovitch - 1929
4 Order-two densities of the image and zero set of stable proc.. (context) - Falconer, Xiao - 1995
4 sided average densities of fractal measures on the line (context) - orters, Preiss et al. - 1995
2 erentiation in the self-ane case III { The density of the Ca.. (context) - Patzschke, ahle et al. - 1993
2 Theory Related Fields (context) - ahle, measures et al. - 1988
1 Geometry of measures in IR ability and densities (context) - Preiss - 1987
1 Recti able measures in IR and existence of principal values .. (context) - Mattila, Preiss - 1995
1 A Local Version of the Projection Theorem and Other Problems.. (context) - O'Neil - 1995
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