Our purpose in this paper is researching about characteristics of convergent in probability and Almost surely convergent in Serstnev space. We prove that if two sequences of random variables are convergent in probability (Almost surely), then, sum, product and scalar product of them are also convergent in probability (Almost surely). Meanwhile, we will prove that each continuous function of every sequence convergent in probability sequence is convergent in probability too. Finally, we represent that for independent random variables, every Almost surely convergent sequence is convergent in probability. In this paper, we conclude results in Serstnev space are similar to probability space.

Lorentz characterized the Almost convergence through the concept of uniform convergence of de la Vallée-Poussin mean. In this paper, we generalize the notion of Almost convergence by using the concept of invariant mean and the generalized de la Vallée-Poussin mean. We determine the bounded linear operators for the generalized s-conservative,  s-regular and s-coercive matrices.

We study new conditions on a radial function f in order to have the Almost everywhere convergence of the spherical partial Fourier integrals.

In this paper, we will discuss the concept of Almost sure convergence for specific groups of fuzzy random variables. For this purpose, we use the type of generalized Chebyshev inequalities. Moreover, we show the concept of Almost sure convergence of weighted average pairwise NQD of fuzzy random variables.

In this paper, we introduce a new type of Almost statistical convergence of generalized difference sequences of fuzzy numbers. We give the relations between the strongly Almost Cesaro type convergence and Almost statistical convergence in these spaces. Furthermore, we study some of their properties like completeness, solidity, symmetricity etc. We also give some inclusion relations related to these classes.

Let {Xn, n³1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1, Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the sequence {Xn, n³1}. Then, we derive uniform strong convergence rates for two-dimensional distribution function of (X1,Xk+1) without any condition on the covariance structure of the variables. Finally, assuming a convenient decrease rate of the covariance’s                                         Cov (X1,Xn+1), n³1we introduce uniform strong convergence rate for covariance function of the limit empirical process.