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Journal of the London Mathematical Society 2004 69(3):801-816; doi:10.1112/S0024610704005319
© 2004 by London Mathematical Society
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© The London Mathematical Society

Exact Packing Measure on the Boundary of a Galton–Watson Tree

Toshiro Watanabe

Center for Mathematical Sciences, University of Aizu Aizu-Wakamatsu 965-8580, Japan, t-watanb{at}u-aizu.ac.jp

Received 13 June 2003. Revision received 10 November 2003.

A necessary and sufficient condition for the almost sure existence of the exact packing measure on the boundary of a Galton–Watson tree is obtained with an explicit exact packing measure. In the case where the exact packing measure does not exist almost surely, a criterion which classifies functions {phi} according to whether the {phi} packing measure is zero or infinity is given.


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