On certain barrelled normed spaces

Valdivia, Manuel. "On certain barrelled normed spaces." Annales de l'institut Fourier 29.3 (1979): 39-56. <http://eudml.org/doc/74425>.

@article{Valdivia1979,
abstract = {Let $\{\cal A\}$ be a $\sigma $-algebra on a set $X$. If $A$ belongs to $\{\cal A\}$ let $e(A)$ be the characteristic function of $A$. Let $\ell ^\infty _0(X,\{\cal A\}$ be the linear space generated by $\lbrace e(A):A \in \{\cal A\}\rbrace $ endowed with the topology of the uniform convergence. It is proved in this paper that if $(E_n)$ is an increasing sequence of subspaces of $\ell ^\infty _0(X,\{\cal A\})$ covering it, there is a positive integer $p$ such that $E_p$ is a dense barrelled subspace of $\ell ^\infty _0(X,\{\cal A\})$, and some new results in measure theory are deduced from this fact.},
author = {Valdivia, Manuel},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {39-56},
publisher = {Association des Annales de l'Institut Fourier},
title = {On certain barrelled normed spaces},
url = {http://eudml.org/doc/74425},
volume = {29},
year = {1979},
}

TY - JOUR
AU - Valdivia, Manuel
TI - On certain barrelled normed spaces
JO - Annales de l'institut Fourier
PY - 1979
PB - Association des Annales de l'Institut Fourier
VL - 29
IS - 3
SP - 39
EP - 56
AB - Let ${\cal A}$ be a $\sigma $-algebra on a set $X$. If $A$ belongs to ${\cal A}$ let $e(A)$ be the characteristic function of $A$. Let $\ell ^\infty _0(X,{\cal A}$ be the linear space generated by $\lbrace e(A):A \in {\cal A}\rbrace $ endowed with the topology of the uniform convergence. It is proved in this paper that if $(E_n)$ is an increasing sequence of subspaces of $\ell ^\infty _0(X,{\cal A})$ covering it, there is a positive integer $p$ such that $E_p$ is a dense barrelled subspace of $\ell ^\infty _0(X,{\cal A})$, and some new results in measure theory are deduced from this fact.
LA - eng
UR - http://eudml.org/doc/74425
ER -