We prove a decomposition theorem of Besicovitch’s type for the relative multifractal Hausdorff measure and packing measure in a probability space. By obtaining a new necessary condition for the strong regularity with the multifractal measures in a more general framework, we extend in this paper the density theorem of Dai and Li (A multifractal formalism in a probability space. Chaos Solitons Fractals...
In this paper, we establish some density results related to the multifractal generalization of the centered Hausdorff and packing measures. We also focus on the exact dimensions of locally finite and Borel regular measures. We, then, apply these theories to a class of Moran sets satisfying the strong separation condition.
The aim of this work is to provide a relationship between the relative multifractal spectra of orthogonal projections of a measure μ in Euclidean space and those of μ. As an application we study the relative multifractal analysis of the projections of a measure.
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