%0 Journal Article
%T SOME CHARACTERIZATIONS ON STATISTICAL
%A OKTAY DUMAN¡è
%A MEHMET G£¿URCAN
%J Journal of Mathematical Analysis
%D 2010
%I 
%X Let (Yn) be a sequence of random variables whose probabilitydistributions depend on x 2 [a; b]: It is well-known that ifnE(Yn   x)2oconverges uniformly to zero on [a; b]; then, for all f 2 C[a; b]; fE (f(Yn))g isuniformly convergent to f on [a; b]; where E denotes the mathematical expecta-tion. In this paper, we mainly improve this result via the concept of statisticalconvergence from the summability theory, which is a weaker method than theusual convergence. Furthermore, we construct an example such that our newresult is applicable while the classical one is not.
%K A-statistical convergence
%K mathematical expectation
%K variance
%K the Chebyshev inequality
%K q-Bernstein polynomials.
%U http://82.114.83.194/ilirias/jma1/repository/docs/JMA2-1-1.pdf