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Gauges for the self-similar sets

✍ Scribed by Sheng-You Wen; Zhi-Xiong Wen; Zhi-Ying Wen

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
152 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

For a self‐similar set E with the open set condition we completely determine the class of its Hausdorff gauges and the class of its prepacking gauges. Moreover, its Hausdorff measures and its packing premeasures with respect to the corresponding gauges are estimated. Without the open set condition we prove that a doubling gauge function is a packing gauge of E if and only if it is a prepacking gauge of E. Also, we give some extensions and applications of these results. Here a gauge function is called a Hausdorff, a prepacking, and a packing gauge of a set, if with respect to the function the set has positive and finite Hausdorff measure, packing premeasure, and packing measure, respectively. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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