Level sets of prevalent Hölder functions

We study the level sets of prevalent H\"older functions. For a prevalent \(\alpha\)-H\"older function on the unit interval, we show that the upper Minkowski dimension of every level set is bounded from above by \(1-\alpha\) and Lebesgue positively many level sets have Hausdorff dimension e...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Anttila, Roope, Bárány, Balázs, Käenmäki, Antti
Format: Article
Language:English
Online Access:Get full text
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Summary:We study the level sets of prevalent H\"older functions. For a prevalent \(\alpha\)-H\"older function on the unit interval, we show that the upper Minkowski dimension of every level set is bounded from above by \(1-\alpha\) and Lebesgue positively many level sets have Hausdorff dimension equal to \(1-\alpha\).
ISSN:2331-8422