Gauges for the self-similar sets

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 w...

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Published inMathematische Nachrichten Vol. 281; no. 8; pp. 1205 - 1214
Main Authors Wen, Sheng-You, Wen, Zhi-Xiong, Wen, Zhi-Ying
Format Journal Article
LanguageEnglish
Published Berlin WILEY-VCH Verlag 01.08.2008
WILEY‐VCH Verlag
Subjects
doubling condition
gauge function
open set condition
Self-similar set
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Summary: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)
Bibliography:NSFC - No. 10771164; No. 10571063; No. 10631040
ArticleID:MANA200510671
ark:/67375/WNG-JWZCVH74-8
Chinese Natural Science Foundation - No. 10571063
istex:7222CC70409EFB576F9712F5F492D52FD9B4E7E3
Phone: +86 27 68766400
Phone: +86 27 88661740 3610
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200510671