Abstract
It has been shown that, from the prevalence point of view, elements of the \(S^\nu \) spaces are almost surely multifractal, while the Hölder exponent at almost every point is almost surely equal to the maximum Hölder exponent. We show here that typical elements of \(S^\nu \) are very irregular by proving that they almost surely satisfy a weak irregularity property: there exists a local irregularity exponent which is constant for almost every element of \(S^\nu \) and equal to the lowest Hölder exponent.
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Clausel, M., Nicolay, S. A Weak Local Irregularity Property in \(S^\nu \) Spaces. Mediterr. J. Math. 14, 102 (2017). https://doi.org/10.1007/s00009-017-0902-1
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DOI: https://doi.org/10.1007/s00009-017-0902-1