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On products of Radon measures

C. Gryllakis, S. Grekas (1999)

Fundamenta Mathematicae

Let X = [ 0 , 1 ] Γ with card Γ ≥ c (c denotes the continuum). We construct two Radon measures μ,ν on X such that there exist open subsets of X × X which are not measurable for the simple outer product measure. Moreover, these measures are strikingly similar to the Lebesgue product measure: for every finite F ⊆ Γ, the projections of μ and ν onto [ 0 , 1 ] F are equivalent to the F-dimensional Lebesgue measure. We generalize this construction to any compact group of weight ≥ c, by replacing the Lebesgue product measure...

On the uniform limit of quasi-continuous functions.

Baltasar Rodríguez-Salinas (2001)

RACSAM

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.

Order convergence of vector measures on topological spaces

Surjit Singh Khurana (2008)

Mathematica Bohemica

Let X be a completely regular Hausdorff space, E a boundedly complete vector lattice, C b ( X ) the space of all, bounded, real-valued continuous functions on X , the algebra generated by the zero-sets of X , and μ C b ( X ) E a positive linear map. First we give a new proof that μ extends to a unique, finitely additive measure μ E + such that ν is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of E + -valued finitely additive measures on are proved, which extend...

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