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

Drewnowski, Lech, and Wnuk, Witold. "On the modulus of measures with values in topological Riesz spaces.." Revista Matemática Complutense 15.2 (2002): 357-400. <http://eudml.org/doc/44375>.

@article{Drewnowski2002,
abstract = {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.},
author = {Drewnowski, Lech, Wnuk, Witold},
journal = {Revista Matemática Complutense},
keywords = {Retículo de Banach; Espacios de Riesz; Medidas vectoriales; Operador débilmente compacto; vector valued measure; topological Riesz space},
language = {eng},
number = {2},
pages = {357-400},
title = {On the modulus of measures with values in topological Riesz spaces.},
url = {http://eudml.org/doc/44375},
volume = {15},
year = {2002},
}

TY - JOUR
AU - Drewnowski, Lech
AU - Wnuk, Witold
TI - On the modulus of measures with values in topological Riesz spaces.
JO - Revista Matemática Complutense
PY - 2002
VL - 15
IS - 2
SP - 357
EP - 400
AB - 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.
LA - eng
KW - Retículo de Banach; Espacios de Riesz; Medidas vectoriales; Operador débilmente compacto; vector valued measure; topological Riesz space
UR - http://eudml.org/doc/44375
ER -