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Packing measure, and its evaluation for a Brownian path. (English) Zbl 0537.28003
A new measure on the subsets $$E\subset {\mathbb{R}}^ d$$ 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 $$R^ d$$ ($$d\geq 3)$$ has finite positive $$\phi$$-packing measure.

##### MSC:
 28A75 Length, area, volume, other geometric measure theory 28A12 Contents, measures, outer measures, capacities 60J65 Brownian motion
##### Keywords:
packing measure; Hausdorff measure; Brownian trajectory
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##### References:
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