Packing Measure, and its Evaluation for a Brownian Path
Open Access
- 1 April 1985
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 288 (2), 679-699
- https://doi.org/10.2307/1999958
Abstract
A new measure on the subsets <!-- MATH $E \subset {{\mathbf{R}}^d}$ --> is constructed by packing as many disjoint small balls as possible with centres in . The basic properties of -packing measure are obtained: many of these mirror those of -Hausdorff measure. For <!-- MATH $\phi (s) = {s^2}/(\log \,\log (1/s))$ --> , it is shown that a Brownian trajectory in <!-- MATH ${{\mathbf{R}}^d}(d \geqslant 3)$ --> has finite positive -packing measure.
Keywords
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