Construction de cocycles en escalier ergodiques et faiblement mélangeants au-dessus de rotations irrationnelles du cercle
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...
Construction of non-constant and ergodic cocycles
We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on the "closure...
Construction of non-subadditive measures and discretization of Borel measures
The main result of the paper provides a method for construction of regular non-subadditive measures in compact Hausdorff spaces. This result is followed by several examples. In the last section it is shown that “discretization” of ordinary measures is possible in the following sense. Given a positive regular Borel measure λ, one may construct a sequence of non-subadditive measures , each of which only takes a finite set of values, and such that converges to λ in the w*-topology.
Constructions of cocycles over irrational rotations
We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.
Constructions of smooth and analytic cocycles over irrational circle rotations
We define a class of step cocycles (which are coboundaries) for irrational rotations of the unit circle and give conditions for their approximation by smooth and real analytic coboundaries. The transfer functions of the approximating (smooth and real analytic) coboundaries are close (in the supremum norm) to the transfer functions of the original ones. This result makes it possible to construct smooth and real analytic cocycles which are ergodic, ergodic and squashable (see [Aaronson, Lemańczyk,...
Continued fractions with sequences of partial quotients over the field of Laurent series
Continuité et différentiabilité des translations dans un espace Gaussien.
Continuity and Extension of Valuations
Continuity and the subdivision norm infimum function
Continuity at zero of semi-groups on L1 and differentiation of additive processes
Continuity of Locally Compact Group Actions with Measurable Orbit Maps.
Continuity properties of solutions of multivalued equations with white noise perturbation.
Continuity Properties of the Extension of a Locally Lipschitz Continuous Map to the Space of Probability Measures.
Continuous additive mappings
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.