Unconditionally Cauchy series and Cesàro summability

In this paper we obtain new characterizations of weakly unconditionally Cauchy series and unconditionally convergent series through Cesàro summability. We study new spaces associated to a series in a Banach space; as a consequence, new characterizations of complete and barrelled normed spaces are proved.     

Permutation-invariance in Komlós type theorem for non-negative random variables

We provide a permutation-invariant version of Komlós’ type convergence for non-negative random variables.