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Sur La Convergence Presque Partout des Suites de Fonctions Mesurables

  • D. Bucchioni (a1) and A. Goldman (a1)

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L'objet de cet article est de donner quelques résultats concernant la structure des suites de fonctions mesurables sur un espace mesuré abstrait (X, ∑, μ), le théorème principal étant le suivant:

Theoreme (A). Soit (ƒn) une suite de fonctions mesurables sur un espace mesuré (X, ∑, μ) dont aucune sous-suite ne converge presque partout. Il existe alors un élément Y ∊ ∑, μ (Y) > 0, deux nombres r ∊ R, δ > 0 et une partie infinie M de N tels que, pour tout A ∊ ∑, ⊂ C F, μ(A) > 0 et pour toute partie infinie L CP.S. M (c'est-à-dire L\M est fini), on puisse trouver x et yA vérifiant ƒn(x) > r + δ et ƒn(y) < r pour une infinité d'indices n ∊ L.

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References

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1. Dor, L. E., On sequences spanning a complex ll space, Proc. Amer. Math. Soc. J+7 (1975), 515516.
2. Fremlin, D. H., Pointwise compact subsets of measurable functions, Manuscripta Math. 15 (1975), 219242.
3. Haydon, R., Some more characterizations of Banach spaces containing ll, Math. Proc. Camb. Phil. Soc. 80 (1976), 269276.
4. Odell, E. et Rosenthal, H. P., A double-dual characterization of separable Banach spaces containing l\ Israël J. Math. 20 (1975), 375384.
5. Rosenthal, H. P., Characterization of Banach spaces containing I1, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 24112413.
6. Rosenthal, H. P., Pointwise compact subsets of the first Baire-class, with some applications to the Banach space theory, Aarhus Universitet, Mathematisk Institut, Various publications, series n°. 24 (1975), 176187.
7. Sazonov, V. V., On perfect measures, Amer. Math. Soc. Transi., (2), 48 (1965), 229254.
8. Talagrand, M., Extensions aux filtres de la mesure de Lebesgue, C. R. Acad. Sci. Paris 283 (1976), 9598.
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Sur La Convergence Presque Partout des Suites de Fonctions Mesurables

  • D. Bucchioni (a1) and A. Goldman (a1)

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