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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
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