Complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination spaces

Strong laws of large numbers for sequences of blockwise and pairwise m-dependent random variables in metris spaces

“…random variables, which extended Theorem 1 of Etemadi [3]. Some more limit theorems for random variables taking values in a convex combination space can be found in Quang and Thuan [6], Thuan et al [9].…”

“…By using a method similar to that used in the proof of Proposition 2.1 of [9], it is easy to show that the concept of Cesàro CUI does not depend on the selected element u 0 . A sequence {X n : n 1} of real-valued random variables is said to be stochastically dominated by a real-valued random variable X if there exists a constant C (0 < C < ∞) such that…”

Baum-Katz’s Type Theorems for Pairwise Independent Random Elements in Certain Metric Spaces

“…random elements [12,Theorem 5.1], which extended [4, Theorem 1] of Etemadi. Since then, some limit theorems for random elements taking values in convex combination space were considered and extended (see [9,11,12,14]). On the other hand, as shown recently in [13], it is fairly remarkable that although these spaces are not linear in general, they always contains a subspace which can be isometrically embedded into a Banach space and this embedding preserves the convex combination operation.…”

Approach for a metric space with a convex combination operation and applications

“…Furthermore, the authors also established the Etemadi strong law of large numbers (SLLN) for normalized sums of pairwise independent, identically distributed (i.i.d.) random elements in this kind of space ( [21], Theorem 5.1), other applications can be found in [18,22,23].…”