On the 1-prevalent continuous functions on compact sets and dimensions

DOI10.1088/1361-6544/acd908OpenAlexW4379794581MaRDI QIDQ6100659

Unnamed Author, Jun Wu, Bo Tan

Publication date: 22 June 2023

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/acd908

zbMATH Keywords

prevalencepacking dimensionupper box dimensiongraph of continuous function1-prevalent

Mathematics Subject Classification ID

Fractals (28A80) Set functions and measures on topological groups or semigroups, Haar measures, invariant measures (28C10)

Cites Work

• Unnamed Item
• Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps
• On the box dimensions of graphs of typical continuous functions
• Dimensions of prevalent continuous functions
• Dimensions of graphs of prevalent continuous maps
• A note on the 1-prevalence of continuous images with full Hausdorff dimension
• Graphs of continuous functions and packing dimension
• The packing dimension of a typical continuous function is 2
• Topological Hausdorff dimension and level sets of generic continuous functions on fractals
• A new fractal dimension: the topological Hausdorff dimension
• The Hausdorff dimension of graphs of prevalent continuous functions
• On sets of Haar measure zero in abelian Polish groups
• The horizon problem for prevalent surfaces
• On the Hausdorff Dimension of Some Graphs
• Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
• Examples of non-shy sets
• Measure and dimension functions: measurability and densities
• Hausdorff Measure and Level Sets of Typical Continuous Mappings in Euclidean Spaces
• Projection theorems for box and packing dimensions
• Dimension and measure for generic continuous images
• Prevalence
• The prevalent dimension of graphs