# Symmetry Properties of Average Densities and Tangent Measure Distributions of Measures on the Line

@article{Mrters1998SymmetryPO, title={Symmetry Properties of Average Densities and Tangent Measure Distributions of Measures on the Line}, author={Peter M{\"o}rters}, journal={Advances in Applied Mathematics}, year={1998}, volume={21}, pages={146-179} }

Answering a question by Bedford and Fisher, we show that for the circular and one-sided average densities of a Radon measure ? on the line with positive lower and finite upper ?-densities, the following relations hold ?-almost everywhere: equation] and equation] 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 and Graf. We show that for…

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