If E is a Banach space with a basis {en}, n belonging to N, a vector measure m: a --> E determines a sequence {mn}, n belonging to N, of scalar measures on a named its components. We obtain necessary and sufficient conditions to ensure that when given a sequence of scalar measures it is possible to construct a vector valued measure whose components were those given. Furthermore we study some relations between the variation of the measure m and the variation of its components.
@article{urn:eudml:doc:38893,
title = {A note on the construction of measures taking their values in a Banach space with basis.},
journal = {Stochastica},
volume = {7},
year = {1983},
pages = {157-161},
zbl = {0577.28004},
mrnumber = {MR0766698},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38893}
}
Congost Iglesias, María. A note on the construction of measures taking their values in a Banach space with basis.. Stochastica, Tome 7 (1983) pp. 157-161. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38893/