# A multifractal formalism for Hewitt-Stromberg measures

## TL;DR

This paper introduces a new multifractal formalism based on Hewitt-Stromberg measures, extending the classical formalism to cases where it does not hold, and parallels Olsen's approach using Hausdorff and packing measures.

## Contribution

It develops a novel multifractal formalism utilizing Hewitt-Stromberg measures, filling gaps where classical methods fail.

## Key findings

- Established a new multifractal formalism for Hewitt-Stromberg measures.
- Demonstrated the formalism's consistency with Olsen's approach.
- Provided theoretical foundations for analyzing measures beyond classical formalisms.

## Abstract

In the present work, we give a new {\it multifractal formalism} for which the classical multifractal formalism does not hold. We precisely introduce and study a multifractal formalism based on the Hewitt-Stromberg measures and that this formalism is completely parallel to Olsen's multifractal formalism which based on the Hausdorff and packing measures.