Constructing a Laplacian on the diamond fractal.
Construction of aggregation operators: new composition method
A new construction method for aggregation operators based on a composition of aggregation operators is proposed. Several general properties of this construction method are recalled. Further, several special cases are discussed. It is also shown, that this construction generalizes a recently introduced twofold integral, which is exactly a composition of the Choquet and Sugeno integral by means of a min operator.
Construction of an Uncountable Difference between Φ(B) and
We construct a set B and homeomorphism f where f and have property N such that the symmetric difference between the sets of density points and of f-density points of B is uncountable.
Construction of functions with prescribed Hölder and chirp exponents.
We show that the Hölder exponent and the chirp exponent of a function can be prescribed simultaneously on a set of full measure, if they are both lower limits of continuous functions. We also show that this result is optimal: In general, Hölder and chirp exponents cannot be prescribed outside a set of Hausdorff dimension less than one. The direct part of the proof consists in an explicit construction of a function determined by its orthonormal wavelet coefficients; the optimality is the direct consequence...
Construction of Measure from Semialgebra of Sets1
In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore, we...
Continued fractions with sequences of partial quotients over the field of Laurent series
Continuity and Extension of Valuations
Continuity and the subdivision norm infimum function
Continuity Properties of the Extension of a Locally Lipschitz Continuous Map to the Space of Probability Measures.
Continuous dependence on parameters of certain self-affine measures, and their singularity
In this paper, we first prove that the self-affine sets depend continuously on the expanding matrix and the digit set, and the corresponding self-affine measures with respect to the probability weight behave in much the same way. Moreover, we obtain some sufficient conditions for certain self-affine measures to be singular.
Continuous-, derivative-, and differentiable-restrictions of measurable functions
We review the known facts and establish some new results concerning continuous-restrictions, derivative-restrictions, and differentiable-restrictions of Lebesgue measurable, universally measurable, and Marczewski measurable functions, as well as functions which have the Baire properties in the wide and restricted senses. We also discuss some known examples and present a number of new examples to show that the theorems are sharp.
Continuous measures and analytic sets
Contracting-on-Average Baker Maps
We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.
Contre-exemples associés aux théorèmes de Rosenthal. Quelques propriétés liées à ces résultats
Contrôle optimal dans des systèmes gouvernés par des inéquations variationnelles
Convergence almost everywhere of sequences of measurable functions
Convergence and submeasures in Boolean algebras
A Boolean algebra carries a strictly positive exhaustive submeasure if and only if it has a sequential topology that is uniformly Fréchet.
Convergence and uniqueness problems for Dirichlet forms on fractals
è un particolare operatore di minimizzazione per forme di Dirichlet definite su un sottoinsieme finito di un frattale che è, in un certo senso, una sorta di frontiera di . Viene talvolta chiamato mappa di rinormalizzazione ed è stato usato per definire su un analogo del funzionale e un moto Browniano. In questo lavoro si provano alcuni risultati sull'unicità dell'autoforma (rispetto a ), e sulla convergenza dell'iterata di rinormalizzata. Questi risultati sono collegati con l'unicità...
Convergence diffuse d'une suite de fonctions
Convergence of ap-Henstock-Kurzweil integral on locally compact spaces
We introduce an ap-Henstock-Kurzweil type integral with a non-atomic Radon measure and prove the Saks-Henstock type lemma. The monotone convergence theorem, -Henstock-Kurzweil equi-integrability, and uniformly strong Lusin condition are discussed.