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2017 A Class of Random Cantor Sets
Changhao Chen
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Real Anal. Exchange 42(1): 79-120 (2017).


In this paper we study a class of random Cantor sets. We determine their almost sure Hausdorff, packing, box, and Assouad dimensions. From a topological point of view, we also compute their typical dimensions in the sense of Baire category. For the natural random measures on these random Cantor sets, we consider their almost sure lower and upper local dimensions. In the end we study the hitting probabilities of a special subclass of these random Cantor sets.


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Changhao Chen. "A Class of Random Cantor Sets." Real Anal. Exchange 42 (1) 79 - 120, 2017.


Published: 2017
First available in Project Euclid: 27 March 2017

zbMATH: 1384.28012
MathSciNet: MR3702557

Primary: 28A80 , 37F40
Secondary: 60D05

Keywords: Baire category, and hitting probabilities , dimensions , random Cantor sets

Rights: Copyright © 2017 Michigan State University Press

Vol.42 • No. 1 • 2017
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