## Packing measure, and its evaluation for a Brownian path

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- by S. James Taylor and Claude Tricot
- Trans. Amer. Math. Soc.
**288**(1985), 679-699 - DOI: https://doi.org/10.1090/S0002-9947-1985-0776398-8
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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.## References

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## Bibliographic Information

- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**288**(1985), 679-699 - MSC: Primary 28A12; Secondary 60J65
- DOI: https://doi.org/10.1090/S0002-9947-1985-0776398-8
- MathSciNet review: 776398