Misure approssimanti ed insiemi ad ampiezza costante
Mixtures of non-atomic measures, II
Möbius fitting aggregation operators
Standard Möbius transform evaluation formula for the Choquet integral is associated with the -aggregation. However, several other aggregation operators replacing operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method...
Modeling, description, and characterization of fractal pore via mathematical morphology.
Modeling snow crystal growth. I: Rigorous results for Packard's digital snowflakes.
Moderation of sigma-finite Borel measures.
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....