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Exact Packing Measure on the Boundary of a Galton–Watson Tree
Author(s) -
Watanabe Toshiro
Publication year - 2004
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/s0024610704005319
Subject(s) - measure (data warehouse) , mathematics , boundary (topology) , tree (set theory) , infinity , zero (linguistics) , combinatorics , mathematical analysis , computer science , linguistics , philosophy , database
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 ϕ according to whether the ϕ packing measure is zero or infinity is given.