Multifractal Formalism and Inequality involving Packing Dimension

TL;DR

This paper develops a new inequality in multifractal analysis that refines existing bounds on packing dimension, with applications demonstrating improved inequalities for specific measure sets.

Contribution

It introduces a novel inequality involving packing dimension that improves upon Olsen's earlier results in multifractal formalism.

Findings

New inequality involving packing dimension $Dim(ar{X}^{eta})$

Application demonstrating improved bounds in specific cases

Refinement of multifractal analysis techniques

Abstract

This article fits in many studies of multifractal analysis of measure. We took as a starting point the work of F. Ben Nasr in " Calculs de dimension de packing " to give a new inequality involving $Dim(\bar{X}^{\alpha})$ which would be, in certain cases, finer than the inequality established by L. Olsen in " A multifractal formalism " . Besides we elaborated an application of our result which gives a better inequality involving $Dim(\bar{X}^{\alpha})$.