Statistical convergence in topological groups

This study consists of the ve chapters. In Section 1 and 2, we give some informations about the historical development of statistical convergence and introduced some fundamental defininitions and theorems which are necessary in this study, respectively. In Section 3, we give defininitions of statistical convergence, strongly Cesàro convergence and lacunary statistical convergence, examine these concepts giving some examples and fundamental defininitions and theorems. In Section 4, we investigate the properties of lacunary statistical convergence in topological groups and relations between statistical convergence, where X is an Abel topological Hausdorf group. In Section 5, we give some theorems of statistical convergence in topological groups. Keywords: Statistical convergence, lacunary convergence, topological group.