Abstract

Let {Xnk,1≤k≤n,n≤1} be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n−1/p∑k=1nXnk,1≤p<2, is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) type p separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.