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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Packing measure, and its evaluation for a Brownian path


Authors: S. James Taylor and Claude Tricot
Journal: Trans. Amer. Math. Soc. 288 (1985), 679-699
MSC: Primary 28A12; Secondary 60J65
MathSciNet review: 776398
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Abstract: A new measure on the subsets $ E \subset {{\mathbf{R}}^d}$ is constructed by packing as many disjoint small balls as possible with centres in $ E$. The basic properties of $ \phi $-packing measure are obtained: many of these mirror those of $ \phi $-Hausdorff measure. For $ \phi (s) = {s^2}/(\log \,\log (1/s))$, it is shown that a Brownian trajectory in $ {{\mathbf{R}}^d}(d \geqslant 3)$ has finite positive $ \phi $-packing measure.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0776398-8
PII: S 0002-9947(1985)0776398-8
Keywords: Packing measure, density theorem, Brownian motion, sojourn time
Article copyright: © Copyright 1985 American Mathematical Society