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Packing Measure Analysis of Harmonic Measure
Author(s) -
Housworth Elizabeth
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/52.3.529
Subject(s) - harmonic measure , measure (data warehouse) , hausdorff measure , mathematics , boundary (topology) , harmonic function , σ finite measure , conformal map , borel measure , harmonic , dimension (graph theory) , domain (mathematical analysis) , mathematical analysis , packing dimension , hausdorff dimension , minkowski–bouligand dimension , pure mathematics , fractal dimension , computer science , probability measure , data mining , fractal , physics , quantum mechanics
We show that, for any Jordan domain J in R 2 , harmonic measure is supported by a Borel set of packing dimension 1. We also obtain incomplete analogs to the results of Makarov, which connect the almost everywhere behavior of the derivative near the boundary for the conformal mapping function from the unit disk → J with the Hausdorff measure properties of sets supporting the harmonic measure.