Packing measure, and its evaluation for a Brownian path

Taylor, S. James; Tricot, Claude

doi:10.1090/S0002-9947-1985-0776398-8

Packing measure, and its evaluation for a Brownian path
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by S. James Taylor and Claude Tricot PDF

Trans. Amer. Math. Soc. 288 (1985), 679-699 Request permission

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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