Modulus of continuity of a set function and some of its applications
Moment matrix of self-similar measures.
Monogenicity of probability measures based on measurable sets invariant under finite groups of transformations
Monotone approximation of measurable multifunctions by simple multifunctions
We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets.
More Lusin properties in the product space
Multiapplications boréliennes à valeurs convexes de
Multidimensional extension of L. C. Young's inequality.
Multidimensional Models for Methodological Validation in Multifractal Analysis
Multifractal analysis is known as a useful tool in signal analysis. However, the methods are often used without methodological validation. In this study, we present multidimensional models in order to validate multifractal analysis methods.
Multidimensional multifractal random measures.
Multidimensional self-affine sets: non-empty interior and the set of uniqueness
Let M be a d × d real contracting matrix. We consider the self-affine iterated function system Mv-u, Mv+u, where u is a cyclic vector. Our main result is as follows: if , then the attractor has non-empty interior. We also consider the set of points in which have a unique address. We show that unless M belongs to a very special (non-generic) class, the Hausdorff dimension of is positive. For this special class the full description of is given as well. This paper continues our work begun...
Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers
We consider the multifractal analysis for Birkhoff averages of continuous potentials on a class of non-conformal repellers corresponding to the self-affine limit sets studied by Lalley and Gatzouras. A conditional variational principle is given for the Hausdorff dimension of the set of points for which the Birkhoff averages converge to a given value. This extends a result of Barral and Mensi to certain non-conformal maps with a measure dependent Lyapunov exponent.
Multifractal analysis of a class of additive processes with correlated non-stationary increments.
Multifractal analysis of infinite products of stationary jump processes.
Multifractal analysis of the divergence of Fourier series
A famous theorem of Carleson says that, given any function , , its Fourier series converges for almost every . Beside this property, the series may diverge at some point, without exceeding . We define the divergence index at as the infimum of the positive real numbers such that and we are interested in the size of the exceptional sets , namely the sets of with divergence index equal to . We show that quasi-all functions in have a multifractal behavior with respect to this definition....
Multifractal dimensions for invariant subsets of piecewise monotonic interval maps
The multifractal generalizations of Hausdorff dimension and packing dimension are investigated for an invariant subset A of a piecewise monotonic map on the interval. Formulae for the multifractal dimension of an ergodic invariant measure, the essential multifractal dimension of A, and the multifractal Hausdorff dimension of A are derived.
Multifractals and projections.
In this paper, we generalize the result of Hunt and Kaloshin [5] about the Lq-spectral dimensions of a measure and that of its projections. The results we obtain, allow to study an untreated case in their work and to find a relationship between the multifractal spectrum of a measure and that of its projections.
Multi-multifractal decomposition of digraph recursive fractals.
In many situations, both deterministic and probabilistic, one is interested in measure theory in local behaviours, for example in local dimensions, local entropies or local Lyapunov exponents. It has been relevant to study dynamical systems, since the study of multifractal can be further developed for a large class of measures invariant under some map, particularly when there exist strange attractors or repelers (hyperbolic case). Multifractal refers to a notion of size, which emphasizes the local...
Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times
By using a wavelet method we prove that the harmonisable-type N-parameter multifractional brownian motion (mfBm) is a locally nondeterministic gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (N, d)-mfBm and to obtain some new results concerning its sample path behavior.
Multiplication, distributivity and fuzzy-integral. I
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.
Multiplication, distributivity and fuzzy-integral. II
Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are...