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The use of packing measure in the analysis of random sets. (English) Zbl 0607.60033
Stochastic processes and their applications, Proc. Int. Conf., Nagoya/Jap. 1985, Lect. Notes Math. 1203, 214-222 (1986).
[For the entire collection see Zbl 0593.00018.]
The author and C. Tricot [Trans. Am. Math. Soc. 288, 679-699 (1985; Zbl 0537.28003)] gave the definition and properties of packing measure with respect to $$\phi$$ (s), a monotone real function. Since $$\phi$$- packing measure is at least as big as Hausdorff $$\phi$$-measure, the fractal index obtained from packing measure, called the packing dimension of a set, is at least as big as the Hausdorff dimension. The present paper obtains the packing dimension of sets defined by the trajectory of a Lévy process in $${\mathbb{R}}^ n$$.

MSC:
 60G17 Sample path properties 28A75 Length, area, volume, other geometric measure theory 60D05 Geometric probability and stochastic geometry