Author
Bilel Selmi
Bio: Bilel Selmi is an academic researcher from University of Monastir. The author has contributed to research in topics: Multifractal system & Hausdorff space. The author has an hindex of 8, co-authored 43 publications receiving 194 citations.
Papers
More filters
TL;DR: In this paper, the relative multifractal spectra of orthogonal projections of a measure in Euclidean space and those of the measure in the orthogonality space were analyzed.
Abstract: 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.
24 citations
TL;DR: In this article, the density results related to the multifractal generalization of the centered Hausdorff and packing measures were established and applied to a class of Moran sets satisfying the strong separation condition.
Abstract: 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.
22 citations
TL;DR: In this paper, the authors defined the upper and lower parameters of the relative multifractal box-dimensions of the measure μ with respect to the measure ν, and investigated the relationship between the multifractual============ rectangle dimension and Hausdorff dimension.
Abstract: 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.
16 citations
15 citations
TL;DR: In this article, a decomposition theorem of Besicovitch's type for the relative multifractal Hausdorff measure and packing measure in a probability space was proved, which is more refined than those found in Dai and Taylor (defining fractal in a probabilistic space).
Abstract: 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 27:57–73, 2006). In particular, this result is more refined than those found in Dai and Taylor (Defining fractal in a probability space. Ill J Math 38:480–500, 1994).
15 citations
Cited by
More filters
410 citations
41 citations
TL;DR: In this article, the density results related to the multifractal generalization of the centered Hausdorff and packing measures were established and applied to a class of Moran sets satisfying the strong separation condition.
Abstract: 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.
22 citations
15 citations
TL;DR: In this article, a decomposition theorem of Besicovitch's type for the relative multifractal Hausdorff measure and packing measure in a probability space was proved, which is more refined than those found in Dai and Taylor (defining fractal in a probabilistic space).
Abstract: 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 27:57–73, 2006). In particular, this result is more refined than those found in Dai and Taylor (Defining fractal in a probability space. Ill J Math 38:480–500, 1994).
15 citations