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