Exact Hausdorff Measure on the Boundary of a Galton–watson Tree

@inproceedings{Watanabe2007ExactHM,
  title={Exact Hausdorff Measure on the Boundary of a Galton–watson Tree},
  author={Taku Watanabe},
  year={2007}
}
A necessary and sufficient condition for the almost sure existence of an absolutely continuous (with respect to the branching measure) exact Hausdorff measure on the boundary of a Galton–Watson tree is obtained. In the case where the absolutely continuous exact Hausdorff measure does not exist almost surely, a criterion which classifies gauge functions φ according to whether φ-Hausdorff measure of the boundary minus a certain exceptional set is zero or infinity is given. Important examples are… CONTINUE READING

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