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Packing dimension and measure of homogeneous Cantor sets

Published online by Cambridge University Press:  17 April 2009

H.K. Baek
H.K. Baek
Affiliation:
Department of Mathematics, Kyungpook National University, Daegu 702–701 South Korea, e-mail: hkbaek@knu.ac.kr
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For a class of homogeneous Cantor sets, we find an explicit formula for their packing dimensions. We then turn our attention to the value of packing measures. The exact value of packing measure for homogeneous Cantor sets has not yet been calculated even though that of Hausdorff measures was evaluated by Qu, Rao and Su in (2001). We give a reasonable lower bound for the packing measures of homogeneous Cantor sets. Our results indicate that duality does not hold between Hausdorff and packing measures.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 3 , December 2006 , pp. 443 - 448
Copyright
Copyright © Australian Mathematical Society 2006

References

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