Continuous linear functionals on the space of Borel vector measures

Pola Siwek. "Continuous linear functionals on the space of Borel vector measures." Annales Polonici Mathematici 93.3 (2008): 199-209. <http://eudml.org/doc/280962>.

@article{PolaSiwek2008,
abstract = {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 $||·||_\{ℱ\}$ 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 $(ℳ,||·||_\{ℱ\})*$ 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.},
author = {Pola Siwek},
journal = {Annales Polonici Mathematici},
keywords = {vector-valued measures; semi-variation; Fortet-Mourier norm},
language = {eng},
number = {3},
pages = {199-209},
title = {Continuous linear functionals on the space of Borel vector measures},
url = {http://eudml.org/doc/280962},
volume = {93},
year = {2008},
}

TY - JOUR
AU - Pola Siwek
TI - Continuous linear functionals on the space of Borel vector measures
JO - Annales Polonici Mathematici
PY - 2008
VL - 93
IS - 3
SP - 199
EP - 209
AB - 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 $||·||_{ℱ}$ 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 $(ℳ,||·||_{ℱ})*$ 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.
LA - eng
KW - vector-valued measures; semi-variation; Fortet-Mourier norm
UR - http://eudml.org/doc/280962
ER -