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

  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},
  • Peter Mörters
  • Published 1 July 1998
  • Mathematics
  • Advances in Applied Mathematics
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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