On the two definitions of independence
D. Ramachandran (1975)
Colloquium Mathematicae
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.
Thomas Riedrich (1980)
Commentationes Mathematicae Universitatis Carolinae
Barbara T. Faires (1976)
Annales de l'institut Fourier
A Boolean algebra has the interpolation property (property (I)) if given sequences , in with for all , there exists an element in such that for all . Let denote an algebra with the property (I). It is shown that if ( a Banach space) is a sequence of strongly additive measures such that exists for each , then defines a strongly additive map from to and the are uniformly strongly additive. The Vitali-Hahn-Saks (VHS) theorem for strongly additive -valued measures defined...
Erik J. Balder, Anna Rita Sambucini (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
In [4, 5, 7] an abstract, versatile approach was given to sequential weak compactness and lower closure results for scalarly integrable functions and multifunctions. Its main tool is an abstract version of the Komlós theorem, which applies to scalarly integrable functions. Here it is shown that this same approach also applies to Pettis integrable multifunctions, because the abstract Komlós theorem can easily be extended so as to apply to generalized Pettis integrable functions. Some results in the...
Szymon Żeberski (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".
Miklós Laczkovich (1999)
Colloquium Mathematicae
Let , and . We show that there is a linear operator such that Φ(f)=f a.e. for every , and Φ commutes with all translations. On the other hand, if is a linear operator such that Φ(f)=f for every , then the group = a ∈ ℝ:Φ commutes with the translation by a is of measure zero and, assuming Martin’s axiom, is of cardinality less than continuum. Let Φ be a linear operator from into the space of complex-valued measurable functions. We show that if Φ(f) is non-zero for every , then must...
S. Aljančić, D. Aranđelović (1977)
Publications de l'Institut Mathématique
N.J. Kaiton, James W. Roberts (1983)
Mathematische Annalen
D.H. Fremlin (1975)
Manuscripta mathematica
G. Vera (1996)
Revista Matemática de la Universidad Complutense de Madrid
In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.
Jürgen Lehn (1977)
Manuscripta mathematica
Rafi, Mohd., Lafuerza-Guillén, B. (2009)
Surveys in Mathematics and its Applications
Josef Štěpán, Pavel Kříž (2010)
Acta Universitatis Carolinae. Mathematica et Physica
Iwo Labuda, R. Daniel Mauldin (1984)
Colloquium Mathematicae
K. Oskolkow (1979)
Banach Center Publications
Zuzana Bukovská (1991)
Mathematica Slovaca
Henri Buchwalter (1977)
Annales de l'institut Fourier
Pour tout compact complètement régulier , on désigne par l’espace des mesures de Radon sur le compactifié de Stone-Cech de et par son sous-espace formé des mesures -régulières au sens de Varadarajan. On décrit alors sur ces deux espaces des topologies , , qui possèdent des propriétés curieuses parmi lesquelles il convient de citer la suivante : pour et pour tout non pseudocompact, l’espace est non quasi-complet mais ses précompacts sont relativement compacts. Ce résultat permet...
Eulalia Grande, Zbigniew Grande (1984)
Fundamenta Mathematicae
Caponetti, D., Trombetta, A., Trombetta, G. (2007)
Journal of Inequalities and Applications [electronic only]