Soit une -algèbre dans un ensemble . Si appartient à , soit la fonction caractéristique de . Soit l’espace vectoriel engendré par avec la topologie de la convergence uniforme. On montre que si est une suite croissante des sous-espaces de dont l’union est il existe un entier positif , telle que est un sous-espace dense et tonnelé de . Quelques nouveaux résultats dans la théorie de la mesure sont déduits de ce fait.
Let be a -algebra on a set . If belongs to let be the characteristic function of . Let be the linear space generated by endowed with the topology of the uniform convergence. It is proved in this paper that if is an increasing sequence of subspaces of covering it, there is a positive integer such that is a dense barrelled subspace of , and some new results in measure theory are deduced from this fact.
@article{AIF_1979__29_3_39_0, author = {Valdivia, Manuel}, title = {On certain barrelled normed spaces}, journal = {Annales de l'Institut Fourier}, volume = {29}, year = {1979}, pages = {39-56}, doi = {10.5802/aif.752}, mrnumber = {81d:46006}, zbl = {0379.46004}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1979__29_3_39_0} }
Valdivia, Manuel. On certain barrelled normed spaces. Annales de l'Institut Fourier, Tome 29 (1979) pp. 39-56. doi : 10.5802/aif.752. http://gdmltest.u-ga.fr/item/AIF_1979__29_3_39_0/
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