Level sets of prevalent H\"older functions

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Abstract

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

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Anttila et al. (Tue,) studied this question.

synapsesocial.com/papers/68e796c9b6db6435877077fb https://doi.org/https://doi.org/10.48550/arxiv.2402.08520

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