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2004-2005 Hausdorff measure of p-Cantor sets.
C. Cabrelli, U. Molter, V. Paulauskas, R. Shonkwiler
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Real Anal. Exchange 30(2): 413-434 (2004-2005).


In this paper we analyze Cantor type sets constructed by the removal of open intervals whose lengths are the terms of the $p$-sequence, $\{k^{-p}\}_{k=1}^\infty$. We prove that these Cantor sets are $s$-sets, by providing sharp estimates of their Hausdorff measure and dimension. Sets of similar structure arise when studying the set of extremal points of the boundaries of the so-called random stable zonotopes.


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C. Cabrelli. U. Molter. V. Paulauskas. R. Shonkwiler. "Hausdorff measure of p-Cantor sets.." Real Anal. Exchange 30 (2) 413 - 434, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

zbMATH: 1124.28008
MathSciNet: MR2177411

Primary: 28A78

Keywords: Cantor like sets , Hausdorff dimension , Hausdorff measure

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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