1985
DOI: 10.2307/1999958
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Packing Measure, and its Evaluation for a Brownian Path

Abstract: A new measure on the subsets £ c It' is constructed by packing as many disjoint small balls as possible with centres in E. The basic properties of ^-packing measure are obtained: many of these mirror those of -Hausdorff measure. For (s) = í2/(loglog(l/í)), it is shown that a Brownian trajectory in R^ (d > 3) has finite positive <¡>-packing measure.

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Cited by 80 publications
(124 citation statements)
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References 5 publications
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“…[15] or [3]. But P t give rise to a Borel measure, namely the t-dimensional packing measure P t (E) of E, as follows…”
Section: Density Theorems For Packing Measures Of Self-similar Setsmentioning
confidence: 99%
See 1 more Smart Citation
“…[15] or [3]. But P t give rise to a Borel measure, namely the t-dimensional packing measure P t (E) of E, as follows…”
Section: Density Theorems For Packing Measures Of Self-similar Setsmentioning
confidence: 99%
“…The packing measure was introduced by Taylor & Tricot in [15] using centered δ-packings of open balls, and by Raymond & Tricot in [11] using centered δ-packings of closed balls. We refer the reader to [16] and [11] for more information on the packing measure and the packing dimension.…”
Section: Density Theorems For Packing Measures Of Self-similar Setsmentioning
confidence: 99%
“…The packing measure and packing dimension, introduced by Tricot [15], Taylor & Tricot [13,14] and Sullivan [12], play an important role in the study of fractal geometry in a manner dual to the Hausdorff measure and Hausdorff dimension (see [9] and [4] for further properties of the above measures and dimensions). However, because of the difficulty in the definition there are few results about the explicit computation of packing measures for fractal sets.…”
Section: Introductionmentioning
confidence: 99%
“…The packing measure and packing dimension were introduced by Tricot [13], Taylor and Tricot [11,12] and Sullivan [10]. As parameters to describe non-smooth sets, the packing measure and packing dimension play an important role in the study of fractal geometry in a manner dual to the Hausdorff measure and Hausdorff dimension (see [3,8] …”
Section: Introductionmentioning
confidence: 99%