Measure theory of statistical convergence (Q1042816)

Statistical convergence has appeared in a wide variety of topics. For different purposes there have been many generalizations of statistical convergence. The question of establishing measure theory for statistical convergence would establish a bridge linking the studies of statistical convergence across measure theory, integration theory, probability and statistics. The authors of this paper show a representation theorem for all finitely additive probability measures defined on the \(\sigma\)-algebra of all the subsets of \(N\), then they give nice properties of classical statistical measures and finally they prove that every kind of statistical convergence is a kind of measure convergence with respect to a specific class of statistical measures.