HAUSDORFF MEASURE OF CARTESIAN PRODUCT OF THE TERNARY CANTOR SET

DOI10.1142/S0218348X12500077zbMath1243.28003OpenAlexW2013764542MaRDI QIDQ2893973

Hui Rao, Zhi-Ying Wen, Juan Deng

Publication date: 27 June 2012

Published in: Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218348x12500077

zbMATH Keywords

Hausdorff measureself-similar setoptimal set

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (9)

Continuous maps that preserve Hausdorff measure ⋮ GAP SEQUENCES OF GRAPH-DIRECTED SETS ⋮ HAUSDORFF MEASURES OF A CLASS OF MORAN SETS ⋮ VISIBILITY OF CARTESIAN PRODUCTS OF CANTOR SETS ⋮ A note on Hausdorff measures of self-similar sets in R^d ⋮ MULTIFRACTAL ANALYSIS OF ONE-DIMENSIONAL BIASED WALKS ⋮ ASYMPTOTIC FORMULA ON AVERAGE PATH LENGTH OF A SPECIAL NETWORK BASED ON SIERPINSKI CARPET ⋮ FRACTALITY OF SUBSTITUTION NETWORKS ⋮ MEAN DISTANCE ON STRETCHED CANTOR PRODUCT

Cites Work

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• The minimum of the upper convex density of the product of the Cantor set with itself
• Self-similar sets with optimal coverings and packings
• Connecting Hausdorff measure and upper convex density or \(H^s\)-a.e. covering
• Exact Hausdorff measure and intervals of maximum density for Cantor sets
• A new estimate of the Hausdorff measure of the Sierpinski gasket
• Computability of the Hausdorff and packing measures on self-similar sets and the self-similar tiling principle
• Twelve open problems on the exact value of the Hausdorff measure and on topological entropy: a brief survey of recent results

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