Geodesic
ON ALMOST SURE CONVERGENCE WITHOUT THE RADON-NIKODYM PROPERTY
Acta mathematica Universitatis Comenianae, Tome 70 (2001) no. 2 
N. Bouzar. ON ALMOST SURE CONVERGENCE WITHOUT THE RADON-NIKODYM PROPERTY. Acta mathematica Universitatis Comenianae, Tome 70 (2001) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2001_70_2_a0/
@article{AMUC_2001_70_2_a0,
     author = {N. Bouzar},
     title = {ON {ALMOST} {SURE} {CONVERGENCE} {WITHOUT} {THE} {RADON-NIKODYM} {PROPERTY}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2001},
     volume = {70},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2001_70_2_a0/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper we obtain almost sure convergence theorems for vector-valued uniform amarts and $C$-sequences without assuming the Radon-Nikodym Property. Specifically, it is shown that if a limit exists in a weak sense for these martingale generalizations, then a.s. scalar and strong convergence follow. These results lead to some new versions of the Ito-Nisio theorem. Convergence results for random sequences taking values in a weakly compact space are also presented.