A Multifractal Formalism for Hewitt–Stromberg Measures

Abstract

In the present work, we give a new 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 is based on the Hausdorff and packing measures.