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.
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.
@article{AIF_1979__29_3_39_0, author = {Valdivia, Manuel}, title = {On certain barrelled normed spaces}, journal = {Annales de l'Institut Fourier}, pages = {39--56}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {29}, number = {3}, year = {1979}, doi = {10.5802/aif.752}, zbl = {0379.46004}, mrnumber = {81d:46006}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.752/} }
TY - JOUR AU - Valdivia, Manuel TI - On certain barrelled normed spaces JO - Annales de l'Institut Fourier PY - 1979 SP - 39 EP - 56 VL - 29 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.752/ DO - 10.5802/aif.752 LA - en ID - AIF_1979__29_3_39_0 ER -
Valdivia, Manuel. On certain barrelled normed spaces. Annales de l'Institut Fourier, Volume 29 (1979) no. 3, pp. 39-56. doi : 10.5802/aif.752. https://aif.centre-mersenne.org/articles/10.5802/aif.752/
[1] Addendum to “FK-spaces containing c0”, Duke Math. J., 39, (1972), 819-821. | MR | Zbl
and ,[2] On a theorem of Nikodym with applications to weak convergence and von Neumann algebra, Pacific Jour. of Math., V. 23, No 3, (1967), 473-477. | MR | Zbl
,[3] Espaces vectoriels topologiques, Departamento de Matemática da Universidade de Sao Paulo, Brasil, 1954. | MR | Zbl
,[4] Exhaustive measures in arbitrary topological vector spaces, Studia Math., LVIII, (1976), 241-248. | MR | Zbl
,[5] Sobre el teorema de la gráfica cerrada, Collectanea Math., XXII, Fasc. 1, (1971), 51-72. | Zbl
,[6] On weak compactness, Studia Math., XLIX, (1973), 35-40. | MR | Zbl
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