We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals on ℳ in some particular cases.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-1,
author = {Pola Siwek},
title = {Continuous linear functionals on the space of Borel vector measures},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {199-209},
zbl = {1154.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-1}
}
Pola Siwek. Continuous linear functionals on the space of Borel vector measures. Annales Polonici Mathematici, Tome 93 (2008) pp. 199-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-1/