On the inner Daniell-Stone and Riesz representation theorems.
On the measures of DiPerna and Majda
DiPerna and Majda generalized Young measures so that it is possible to describe “in the limit” oscillation as well as concentration effects of bounded sequences in -spaces. Here the complete description of all such measures is stated, showing that the “energy” put at “infinity” by concentration effects can be described in the limit basically by an arbitrary positive Radon measure. Moreover, it is shown that concentration effects are intimately related to rays (in a suitable locally convex geometry)...
On the setwise convergence of sequences of measures.
On the uniform limit of quasi-continuous functions.
Estudiamos cuando el límite uniforme de una red de funciones cuasi-continuas con valores en un espacio localmente convexo X es también una función cuasi-continua, resaltando que esta propiedad depende del menor cardinal de un sistema fundamental de entornos de O en X, y estableciendo condiciones necesarias y suficientes. El principal resultado de este trabajo es el Teorema 15, en el que los resultados de [7] y [10] son mejorados, en relación al Teorema de L. Schwartz.
On uniformly regular measures
On various notions of regularity in ordered spaces
On weakly convergent nets in spaces of non-negative measures
Order convergence of vector measures on topological spaces
Let be a completely regular Hausdorff space, a boundedly complete vector lattice, the space of all, bounded, real-valued continuous functions on , the algebra generated by the zero-sets of , and a positive linear map. First we give a new proof that extends to a unique, finitely additive measure such that is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of -valued finitely additive measures on are proved, which extend...
Outer measure analysis of topological lattice properties.
Outer measures and associated lattice properties.
Outer measures and weak regularity of measures.
Outer measures associated with lattice measures and their application.
Outer measures, measurability, and lattice regular measures.
Pairwise Borel and Baire measures in bispaces
In this paper we continue the study of the concepts of pairwise Borel and Baire measures in a bispace, recently introduced in [10]. We investigate some of its consequences including the problem of a pairwise regular Borel extension of a pairwise Baire measure.
Positivity principle for more concentrated measures.
Product of vector measures on topological spaces
For , let be completely regular Hausdorff spaces, quasi-complete locally convex spaces, , the completion of the their injective tensor product, the spaces of all bounded, scalar-valued continuous functions on , and -valued Baire measures on . Under certain...
Products of completion regular measures
We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.
Projective limits of vector measures.
A necessary and sufficient condition for the existence of the projective limit of measures with values in a locally convex space is given. A similar theorem for measures with values in different locally convex spaces (under certain conditions) is given too (in this case, the projective limit is valued in the projective limit of these spaces). Finally, a result about the projective limit of vector measures is stated.
Properties of the class of measure separable compact spaces
We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure...
Proprites de Radon-Nikodym pour les cones positifs de mesures.