On the modulus of measures with values in topological Riesz spaces.

Título inglés On the modulus of measures with values in topological Riesz spaces.
Título español Sobre el módulo de medidas con valores en espacios topológicos de Riesz.
Autor/es Drewnowski, Lech ; Wnuk, Witold
Organización Fac. Math Comput. Sci. A. Mickiewicz Univ., Poznan, Polonia
Revista 1139-1138
Publicación 2002, 15 (2): 357-400, 35 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés The paper is devoted to a study of some aspects of the theory of (topological) Riesz space valued measures. The main topics considered are the following. First, the problem of existence (and, particularly, the so-called proper existence) of the modulus of an order bounded measure, and its relation to a similar problem for the induced integral operator. Second, the question of how properties of such a measure like countable additivity, exhaustivity or so-called absolute exhaustivity, or the properties of the range space, influence the properties of the modulus of the measure. Third, the problem of exhibiting (or constructing) Banach lattices that are good'' in many respects, and yet admit a countably additive measure whose modulus is not countably additive. A few applications to weakly compact operators from spaces of bounded measurable functions to Banach lattices are also presented.
Clasificación UNESCO 120203
Palabras clave español Retículo de Banach ; Espacios de Riesz ; Medidas vectoriales ; Operador débilmente compacto
Código MathReviews MR1951817
Código Z-Math Zbl 1035.46031
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