| Let {X(,nk) : 1 (LESSTHEQ) k (LESSTHEQ) n, n (GREATERTHEQ) 1} be an arrary of row-wise exchangeable random elements in a separable Banach space X. For each continuous linear functional f in the dual space of X, a measure of nonorthogonality is generally given by (rho)(,n) = E{f(X(,n1))f(X(,n2))}. Using martingale techniques and a condition on the measure of nonorthogonality, a strong law of large numbers is obtained for triangular arrays of random variables that are row-wise exchangeable. Strong convergence results are similarly obtained for the weighted sum.;where {a(,nk)} is an array of constants. Using similar conditions as above and a condition involving tightness of distributions and moments of random elements, a strong convergence result for arrays of random elements that are tight and row-wise exchangeable is obtained.;Convergence in the r('th) mean of each column in the triangular array of row-wise exchangeable random elements generates an infinite sequence of exchangeable random elements. With the condition of mean convergence and a condition of nonorthogonality, strong convergence results are obtained for triangular arrays of row-wise exchangeable random elements in arbitrary and Rademacher type p + (delta) separable Banach spaces. Under similar conditions, strong convergence results are obtained for the randomly weighted sum.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;where {a(,nk)} is an array of random variables. |
