Abstract
It will be shown and induced that thed-dimensional indices in the Banach spaces version conditions∑n(E‖Xn‖p/|nα|p)<∞are sufficient to yieldlimmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=0a.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.
Subject
Mathematics (miscellaneous)