A Review on Multifractal Analysis of Hewitt-Stromberg Measures

We estimate the upper and lower bounds of the Hewitt-Stromberg dimensions. In particular, these results give new proofs of theorems on the multifractal formalism which is based on the Hewitt-Stromberg measures and yield results even at points q for which the upper and lower multifractal Hewitt-Stromberg dimension functions differ. Finally, concrete examples of a measure satisfying the above property are developed.

Automated summary

We estimate the upper and lower bounds of the Hewitt-Stromberg dimensions, which provides new proofs of theorems on the multifractal formalism based on Hewitt-Stromberg measures. We also provide concrete examples of measures satisfying the above property.