Journal ArticleDOI
Multifractal variation for projections of measures
Zied Douzi,Bilel Selmi +1 more
Reads0
Chats0
TLDR
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.read more
Citations
More filters
Journal ArticleDOI
Some density results of relative multifractal analysis
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.
Journal ArticleDOI
A Multifractal Formalism for Hewitt–Stromberg Measures
Najmeddine Attia,Bilel Selmi +1 more
TL;DR: In this article, a new multifractal formalism based on the Hewitt-Stromberg measures was proposed, which is completely parallel to Olsen's FSM, based on Hausdorff and packing measures.
Posted ContentDOI
Multifractal dimensions for projections of measures
TL;DR: In this article, Dai et al. studied the multifractal Hausdorff and packing dimensions of Borel probability measures and studied their behaviors under orthogonal projections, and improved the main result of Dai in \cite{D} about the multifractal analysis of a measure of multifractual exact dimension.
Journal ArticleDOI
On the effect of projections on the Billingsley dimensions
TL;DR: In this article, the behavior of Billingsley dimensions under projections onto a lower dimensional linear subspace was studied and connections with various dimensions were established with respect to the connections between different dimensions.
Journal ArticleDOI
A relative multifractal analysis
TL;DR: In this paper, a general formalism for the multifractal analysis of one probability measure with respect to another is introduced, and the analysis of the structure of quasi-Bernoulli and homogeneous Moran measures is studied.
References
More filters
Book
Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
Book
The geometry of fractal sets
TL;DR: In this paper, a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension is presented, including questions of local density and the existence of tangents of such sets, and the dimensional properties of their projections in various directions.
Journal ArticleDOI
A Multifractal Formalism
TL;DR: In this paper, the authors show that fμ(Fμ) is bounded from above by the Legendre transform of bμBμ) and that equality holds for graph directed self-similar measures and "cookie-cutter" measures.
Journal ArticleDOI
On Hausdorff dimension of projections
TL;DR: In this paper, it was shown that if s ≤ 1 then Ft has dimension ≥ s, excepting numbers t in a set of dimension ≤ s, and if s > 1, Ft has positive Lebesgue measure, except for numbers t ∈ the set of lebesgue measures 0.