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Relative multifractal box-dimensions

Attia Najmeddine (Faculté des Sciences de Monastir, Département de Mathématiques, Monastir, Tunisia)
Selmi Bilel (Faculté des Sciences de Monastir, Département de Mathématiques, Monastir, Tunisia)

Given two probability measures μ and ν on Rn. We define the upper and lower relative multifractal box-dimensions of the measure μ with respect to the measure ν and investigate the relationship between the multifractal box-dimensions and the relative multifractal Hausdorff dimension, the relative multifractal pre-packing dimension. We also, calculate the relative multifractal spectrum and establish the validity of multifractal formalism. As an application, we study the behavior of projections of measures obeying to the relative multifractal formalism.

Keywords: Relative Hausdorff dimension, Relative packing dimension, Relative multifractal analysis