On Almost Sure Convergence without the Radon-nikodym Property
نویسنده
چکیده
In this paper we obtain almost sure convergence theorems for vectorvalued 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.
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تاریخ انتشار 2001