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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 inner Daniell-Stone and Riesz representation theorems.

König, Heinz (2000)

Documenta Mathematica

On the relation between the multidimensional moment problem and the one-dimensional moment problem.

L.C. Petersen (1982)

Mathematica Scandinavica

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.

On various notions of regularity in ordered spaces

Peter Volauf (1985)

Mathematica Slovaca

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 $X$ , $ℱ$ the algebra generated by the zero-sets of $X$ , and $μ C_{b} (X) \to E$ a positive linear map. First we give a new proof that $μ$ extends to a unique, finitely additive measure $μ ℱ \to E^{+}$ 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 $ℱ$ are proved, which extend...

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