On some generic small Cantor spaces

DOI10.4171/ZAA/1660zbMath1446.28003arXiv1905.07184OpenAlexW2981574132MaRDI QIDQ2197920

Martina Maiuriello, D'Aniello, Emma

Publication date: 1 September 2020

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.07184

zbMATH Keywords

Hausdorff dimensionBaire categoryCantor spacemicroscopic set

Mathematics Subject Classification ID

Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Baire category, Baire spaces (54E52) Length, area, volume, other geometric measure theory (28A75)

Related Items (2)

A Cantor-type construction. Invariant set and measure ⋮ On dynamics of families of equi-Baire one functions on metric spaces

Cites Work

• Homeomorphisms of linear and planar sets of the first category into microscopic sets
• Attractors for iterated function schemes on \([0, 1^N\) are exceptional]
• Microscopic and strongly microscopic sets on the plane. Fubini theorem and Fubini property
• Chaos in terms of the map \(x\to\omega(x,f)\)
• Nowhere monotone functions and microscopic sets
• General approach to microscopic-type sets
• Non-self-similar sets in \([0,1^{N}\) of arbitrary dimension]
• Some remarks on small sets
• Hausdorff dimension of symmetric perfect sets
• Families of symmetric Cantor sets from the category and measure viewpoints
• A generalization of the notion of microscopic sets
• Fubini Property for Microscopic Sets
• Microscopic Sets with Respect to Sequences of Functions
• On microscopic sets and Fubini Property in all directions
• EXACT HAUSDORFF MEASURE OF CERTAIN NON-SELF-SIMILAR CANTOR SETS
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