A weak local irregularity property in S^\nu spaces

TL;DR

This paper demonstrates that elements of S^ν spaces, known for their multifractal nature, also almost surely exhibit a weak uniform irregularity property, revealing a new aspect of their structure.

Contribution

It introduces the almost sure presence of a weak uniform irregularity property in S^ν spaces, expanding understanding of their multifractal characteristics.

Findings

Elements of S^ν spaces are almost surely multifractal.

They also almost surely satisfy a weak uniform irregularity property.

This reveals a new structural aspect of S^ν spaces.

Abstract

Although it has been shown that, from the prevalence point of view, the elements of the S^ \nu spaces are almost surely multifractal, we show here that they also almost surely satisfy a weak uniform irregularity property.