Dimensions of prevalent continuous functions

DOI10.1007/s00605-011-0365-6zbMath1251.28005OpenAlexW2103489795MaRDI QIDQ420591

V. Mijović, O. Ng, L. Olsen, Vytautas Gruslys, Julius Jonušas, Izabela Petrykiewicz

Publication date: 22 May 2012

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-011-0365-6

zbMATH Keywords

prevalencebox dimensionHölder exponentmultifractalRenyi dimensionshyness

Mathematics Subject Classification ID

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

Related Items (10)

On the graphs of products of continuous functions and fractal dimensions ⋮ On the 1-prevalent continuous functions on compact sets and dimensions ⋮ Graphs of continuous functions and packing dimension ⋮ ON THE DECOMPOSITION OF CONTINUOUS FUNCTIONS AND DIMENSIONS ⋮ Haar null and Haar meager sets: a survey and new results ⋮ ON A CONJECTURE REGARDING THE UPPER GRAPH BOX DIMENSION OF BOUNDED SUBSETS OF THE REAL LINE ⋮ On the Hausdorff Dimension of Graphs of Prevalent Continuous Functions on Compact Sets ⋮ A survey on prescription of multifractal behavior ⋮ A note on the 1-prevalence of continuous images with full Hausdorff dimension ⋮ Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps

Cites Work

• On the box dimensions of graphs of typical continuous functions
• Some generic properties in analysis,
• How smooth is almost every function in a Sobolev space?
• On generators of shy sets on Polish topological vector spaces
• The packing dimension of a typical continuous function is 2
• Applications of the Baire category theorem
• The Sobolev embeddings are usually sharp
• On sets of Haar measure zero in abelian Polish groups
• On the Hausdorff Dimension of Some Graphs
• Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
• Generic Validity of the Multifractal Formalism
• Prevalence
• Wavelets
• The prevalent dimension of graphs
• Shyness of sets in the space of automorphisms on \([0,1\)]
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Dimensions of prevalent continuous functions