A Best Covering Problem.
A Borel extension approach to weakly compact operators on
Let be a quasicomplete locally convex Hausdorff space. Let be a locally compact Hausdorff space and let , is continuous and vanishes at infinity be endowed with the supremum norm. Starting with the Borel extension theorem for -valued -additive Baire measures on , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map to be weakly compact.
A Borel topos
A Cantor regular set which does not have Markov's property
A Cantor set in the plane that is not σ-monotone
A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.
A categorical approach to integration.
A category analogue of the density topology
A category Ψ-density topology
Ψ-density point of a Lebesgue measurable set was introduced by Taylor in [Taylor S.J., On strengthening the Lebesgue Density Theorem, Fund. Math., 1958, 46, 305–315] and [Taylor S.J., An alternative form of Egoroff’s theorem, Fund. Math., 1960, 48, 169–174] as an answer to a problem posed by Ulam. We present a category analogue of the notion and of the Ψ-density topology. We define a category analogue of the Ψ-density point of the set A at a point x as the Ψ-density point at x of the regular open...
A central limit theorem for processes generated by a family of transformations [Book]
A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space. II.
A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space.
A chaotic function with zero topological entropy having a non-perfect attractor
A characterization and moving average representation for stable harmonizable processes.
A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources
We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order concentrated on an -neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.
A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources
We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order concentrated on an ε-neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.
A characterization of group-valued measures satisfying the countable chain condition
A characterization of Jordan and Lebesgue measures
A characterization of partition polynomials and good Bernoulli trial measures in many symbols
Consider an experiment with d+1 possible outcomes, d of which occur with probabilities . If we consider a large number of independent occurrences of this experiment, the probability of any event in the resulting space is a polynomial in . We characterize those polynomials which arise as the probability of such an event. We use this to characterize those x⃗ for which the measure resulting from an infinite sequence of such trials is good in the sense of Akin.
A characterization of regular averaging operators and its consequences
We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain...
A characterization of space-filling curves.
En este artículo revisamos un famoso teorema, descubierto por H. Steinhaus en 1936, en el que se da una condición suficiente que permite obtener las funciones coordenadas de una curva que llena el cuadrado unidad. Ponemos de manifiesto que el recíproco de este teorema no se cumple para la curva de Lebesgue. Aquí proponemos un teorema de caracterización de curvas que llenan el espacio, basado en una condición de llenado. Asimismo, damos una caracterización constructiva de esta condición de llenado...