On vector measures

Constantinescu, Corneliu. "On vector measures." Annales de l'institut Fourier 25.3-4 (1975): 139-161. <http://eudml.org/doc/74238>.

@article{Constantinescu1975,
abstract = {Let $\{\cal M\}$ be the Banach space of real measures on a $\sigma $-ring $\{\bf R\}$, let $\{\cal M\}^\{\prime \}$ be its dual, let $E$ be a quasi-complete locally convex space, let $E^\{\prime \}$ be its dual, and let $\mu $ be an $E$-valued measure on $\{\bf R\}$. If is shown that for any $\theta \in \{\cal M\}^\{\prime \}$ there exists an element $\int \theta \ d\mu $ of $E$ such that $\langle x^\{\prime \}\circ \mu ,\theta \rangle = \big \langle \int \theta \ d\mu ,x^\{\prime \}\big \rangle $ for any $x^\{\prime \}\in E^\{\prime \}$ and that the map\begin\{\}\theta \rightarrow \int \theta \ d\mu : \{\cal M\}^\{\prime \} \rightarrow E\end\{\}is order continuous. It follows that the closed convex hull of $\mu (\{\bf R\})$ is weakly compact.},
author = {Constantinescu, Corneliu},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3-4},
pages = {139-161},
publisher = {Association des Annales de l'Institut Fourier},
title = {On vector measures},
url = {http://eudml.org/doc/74238},
volume = {25},
year = {1975},
}

TY - JOUR
AU - Constantinescu, Corneliu
TI - On vector measures
JO - Annales de l'institut Fourier
PY - 1975
PB - Association des Annales de l'Institut Fourier
VL - 25
IS - 3-4
SP - 139
EP - 161
AB - Let ${\cal M}$ be the Banach space of real measures on a $\sigma $-ring ${\bf R}$, let ${\cal M}^{\prime }$ be its dual, let $E$ be a quasi-complete locally convex space, let $E^{\prime }$ be its dual, and let $\mu $ be an $E$-valued measure on ${\bf R}$. If is shown that for any $\theta \in {\cal M}^{\prime }$ there exists an element $\int \theta \ d\mu $ of $E$ such that $\langle x^{\prime }\circ \mu ,\theta \rangle = \big \langle \int \theta \ d\mu ,x^{\prime }\big \rangle $ for any $x^{\prime }\in E^{\prime }$ and that the map\begin{}\theta \rightarrow \int \theta \ d\mu : {\cal M}^{\prime } \rightarrow E\end{}is order continuous. It follows that the closed convex hull of $\mu ({\bf R})$ is weakly compact.
LA - eng
UR - http://eudml.org/doc/74238
ER -