The aim of this paper is to establish some strong laws of large numbers and -convergence for double arrays of random elements in p-uniformly smooth Banach spaces. We also provide a new characterization of p-uniformly smooth Banach spaces in terms of a strong law of large numbers for double arrays.

The aim of this paper is to establish the noncommutative versions of the degenerate convergence criterion and Feller’s weak law of large numbers for adapted double arrays.

In this paper, we state several convergence results with respect to the Mosco topology of strong laws of large numbers for triangular arrays of rowwise independent random sets in a separable Banach space of type p(1<p≤2). We also provide some typical examples illustrating this study.

We consider a new family of convex weakly compact valued integrable random sets which is called an adapted array of convex weakly compact valued integrable random variables of type p (1⩽p⩽2). By this concept, more general laws of large numbers will be established. Some illustrative examples...