Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements
نویسنده
چکیده
It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑ n(E‖Xn‖/|n|) < ∞ are sufficient to yield limmin1≤ j≤d(nj)→∞(1/ |nα|)∑k≤n ∏d j=1(1− (kj − 1)/nj)Xk = 0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that there are the best possible sufficient conditions for multi-indexed independent real-valued random variables.
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ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2007 شماره
صفحات -
تاریخ انتشار 2007