On the Construction of Almost Uniformly Convergent Random Variables with Given Weakly Convergent Image Laws

On the Spaces of $lambda _{r}$-almost Convergent and $lambda _{r}$-almost Bounded Sequences

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...

On Lacunary Almost Convergent Sequences

The purpose of this paper is to define and study the spaces [ĉ,M, p](∆u , q, s), [ĉ,M, p, ] θ 0(∆ m u , q, s) and [ĉ,M, p, ] θ ∞(∆ m u , q, s) of lacunary convergent sequences. We also study some inclusion relations between these spaces and some properties and theorems. 2000 Mathematics Subject Classification:40D05, 40A05. 1.Introduction and definitions Let w denote the set of all complex seque...

ON THE LAWS OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES

In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.

Tail sums of convergent series of independent random variables

On the Summation of a Particular Non-uniformly-convergent Series

In a previous article the force between a dielectric cylinder and a conducting half-space for the cylinder approaching the half-space was obtained as the limit of a non-uniformly-convergent series. A special asymptotic analysis was performed to get a closed-form solution for this limit. The present article focuses on a delicate and crucial step in this analysis and gives a justification by a ma...